3 - A small shelter for delicate plants is to be... Ch. 3.4 - Show that the equation x5x4x35x212x6=0 has exactly... Ch. 3 - Graph the polynomial P(x) = (x + 2)3 + 27, showing... Ch. 3.2 - Graph the family of polynomials in the same... Ch. 3.4 - Show that the polynomial does not have any... Ch. This example has a double root. 3.4 - Using Descartes Rule of Signs, we can tell that... Ch. The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial. 3.7 - Graph the rational function f, and determine all... Ch. 3.6 - actor the polynomial completely, and find all its... Ch. 3.6 - By the Zeros Theorem, every n th-degree polynomial... Ch. Subscribe to bartleby learn! The polynomial of the specified degree can be, P(x)=(x+2)(x+2)(x−1)(x−1)P(x)=(x+2)2(x−1)2P(x)=(x2+4x+4)(x2−2x+1)P(x)=x4+2x3−3x2−4x+4. Find the zeros of a polynomial function. (a) Determine... Ch. What are the real and... Ch. Comparing Smooth and Continuous Graphs. 3.6 - Find a polynomial with integer coefficients that... Ch. 3 - Clothing Sales Are Seasonal Clothing sales tend to... Ch. 3.3 - Find a polynomial of degree 4 that has integer... Ch. 3 - State the Fundamental Theorem of Algebra. P(x)=2x38x2+9x9, Ch. 3.4 - True or False? To recall, a polynomial is defined as an expression of more than two algebraic terms, especially the sum (or difference) of several terms that contain different powers of the same or different variable(s). 3.1 - Find a function whose graph is a parabola with... Ch. By using this website, you agree to … The least possible even multiplicity is 2. 3 - A polynomial P is given. X-intercept. P(x)=x5+x3+8x2+8... Ch. 3 - Find the quotient and remainder. Graphs of polynomials: Challenge problems Our mission is to provide a free, world-class education to anyone, anywhere. 3.1 - Maximizing Profit A community bird-watching... Ch. 3 - State the Division Algorithm and identify the... Ch. x42x2+7xx2x+3. 3.6 - Find all zeros of the polynomial. 3.5 - Find all solutions of the equation and express... Ch. We are graphing first since the method for finding all the zeroes of a polynomial can be a little long and we don’t want to obscure the details of this section in the mess of finding the zeroes of the polynomial. If you liked this video please like, share, comment, and subscribe. Ch. 3 - Graph the rational function. To sketch any polynomial function, you can start by finding the real zeros of the function and end behavior of the function . What steps would... Ch. 3.1 - Find all local maximum and minimum values of the... Ch. No! x23x+5x2, Ch. Help me help as many students with math as possible.Math with Mr. Barnes is a math video tutorial channel meant to help students with math. 3.2 - Match the polynomial function with one of the... Ch. 3.3 - Let P(x)=6x740x6+16x5200x460x369x2+13x139... Ch. 3.2 - Which of the following statements couldnt possibly... Ch. 3 - Find the quotient and remainder. 3.3 - Find the quotient and remainder using synthetic... Ch. There may be parts that are steep or very flat. 3.1 - Maximum of a Fourth-Degree Polynomial Find the... Ch. 3.5 - The imaginary number i has the property that i2=. 3.1 - The graph of f(x) = 3(x - 2)2 - 6 is a parabola... Ch. Question 4: The graph below cuts the x axis at x = -1. (a) Use... Ch. 3.2 - Sketch the graph of the polynomial function. Use either... Ch. Example: what is the degree of this polynomial: 4z 3 + 5y 2 z 2 + 2yz. A polynomial function of degree has at most turning points. 3.2 - Graph the polynomial and determine how many local... Ch. 3.1 - Sales A soft-drink vendor at a popular beach... Ch. 3.1 - Find the local maximum and minimum values of the... Ch. 3.6 - Polynomials of Odd Degree The Conjugate Zeros... Ch. Ch. 3.6 - Find all zeros of the polynomial. It can calculate and graph the roots (x-intercepts), signs , local maxima and minima , increasing and decreasing intervals , points of inflection and concave up/down intervals . Polynomial graphing calculator This page help you to explore polynomials of degrees up to 4. If c is a real zero of the... Ch. (a) List all possible... Ch. 3 - Find the quotient and remainder. Answer to Problem 67E The polynomial of degree 4 that has the given zeros as shown in the graph is, 3.1 - Making a Rain Gutter A rain gutter is formed by... Ch. 3 - Find a polynomial of degree 3 with constant... Ch. Finding the roots of a polynomial equation, for example . Graph the polynomial and see where it crosses the x-axis. 3.1 - Stadium Revenue A baseball team plays in a stadium... Ch. Is it possible for a... Ch. State the Factor... Ch. f(x) = x 4 − x 3 − 19x 2 − 11x + 31 is a polynomial function of degree 4. 3 - How Fast Can You List Your Favorite Things? (a) Express the... Ch. 2. Roots of an Equation. If a is an upper bound for the real... Ch. Figure 3: Graph of a third degree polynomial Polynomial of a third degree polynomial: one x intercepts. 3.6 - A polynomial of degree n 1 has exactly ________... Ch. One minute you could be running up hill, then the terrai… 3.6 - Factor the polynomial completely, and find all its... Ch. Find the polynomial of the specified degree whose graph is shown. 3.2 - If c is a zero of the polynomial P, which of the... Ch. 3.6 - The polynomial P(x)=3(x5)3(x3)(x+2) has degree... Ch. The largest possible number of minimum or maximum points is one less than the degree of the polynomial. 3 - What steps would you follow to graph a polynomial... Ch. 3.3 - (a) If we divide the polynomial P(x) by the factor... Ch. 3.4 - Find all the real zeros of the polynomial. If you... Ch. Make... Ch. To find the degree of a polynomial: Add up the … 3.4 - List all possible rational zeros given by the... Ch. x 4 − x 3 − 19x 2 − 11x + 31 = 0, means "to find values of x which make the equation true." 3.1 - Height of a Ball If a ball is thrown directly... Ch. The following examples illustrate several possibilities. To answer this question, I have to remember that the polynomial's degree gives me the ceiling on the number of bumps. (a) Factor P into linear... Ch. 3.7 - Drug Concentration After a certain drug is... Ch. (a) Find all zeros of P,... Ch. P(x)=x3+2x2+4x+8, Ch. For example, if you have found the zeros for the polynomial f(x) = 2x4 – 9x3 – 21x2 + … 3.3 - Find a polynomial of the specified degree that has... Ch. 3 - Too Many Corn Plants per Acre? 3.4 - Let P(x) be a polynomial with real coefficients... Ch. x3x2+11x+2x4, Ch. 3.7 - Focusing Distance For a camera with a lens of... Ch. 3.2 - Population Change The rabbit population on a small... Ch. 3.2 - Graph the function P(x)=(x2)(x4)(x5) and determine... Ch. 3 - Find a fourth-degree polynomial with integer... Ch. We can also identify the sign of the leading coefficient by observing the end behavior of the function. 3 - Find the indicated value of the polynomial using... Ch. 3.7 - Graphs with Holes In this chapter we adopted the... Ch. 3.5 - The complex conjugate of 3+4i is 3+4i=. 3 - Find the quotient and remainder. Predict the end behavior of the function. 3 - Find a polynomial of degree 4 that has integer... Ch. 3 - Evaluate the expression and write in the form... Ch. 3.2 - Volume of a Box A cardboard box has a square base,... Ch. 3 - Write the defining equation for a polynomial P of... Ch. P(x)=x32x2+2x1. (a) Complete each... Ch. (a) Find all the real... Ch. 3.2 - Sketch the graph of each function by transforming... Ch. In each case, the accompanying graph is shown under the discussion. 3 - What is a rational function? 3.5 - Recall that the symbol z represents the complex... Ch. 3.4 - Find all rational zeros of the polynomial, and... Ch. 3 - Let P(x) = 2x4 7x3 + x2 18x + 3. 2x3+x28x+15x2+2x1, Ch. 3.4 - The real solutions of the given equation are... Ch. A polynomial function of degree $$n$$ has at most $$n−1$$ turning points. This lesson will explain the graph of a polynomial function by identifying properties including end behavior, real and non-real zeros, odd and even degree, and relative maxima or minima. 3.7 - From the graph, determine the x- and y-intercepts... Ch. The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7. 3.2 - Factor the polynomial and use the factored form to... Ch. 3.1 - Advertising The effectiveness of a television... Ch. 3 - Sketch graphs showing the possible end behaviors... Ch. 3.5 - Powers of i Calculate the first 12 powers of $i,$... Ch. Identify a polynomial function. 3 - A cannonball fired out to sea from a shore battery... Ch. If r is a zero of even multiplicity, then the graph touches the x-axis and _____ at r. If r is a zero of odd multiplicity, then the graph _____ the x-axis at r. 3 - Show that 12 is a zero of the polynomial... Ch. Show clearly all x-... Ch. As a review, here are some polynomials, their names, and their degrees. The degree of a polynomial is the highest power of the variable in a polynomial expression. 3.2 - Every polynomial has one of the following... Ch. 3.2 - On the same coordinate axes, sketch graphs (as... Ch. 3.6 - Find all zeros of the polynomial. Finding the Equation of a Polynomial from a Graph - YouTube What does it mean to... Ch. 3.2 - Portions of the graphs of y=x2,y=x3,y=x4,y=x5, and... Ch. 3 - (a) Use synthetic division to find the quotient... Ch. 3 - Find all rational, irrational, and complex zeros... Ch. A polynomial is generally represented as P(x). Standard form: P(x) = a₀ where a is a constant. 3.3 - Find a polynomial of degree 3 that has zeros 1,2,... Ch. 3.7 - The following questions are about the rational... Ch. 3.4 - Use a graphing device to find all real solutions... Ch. 3.4 - A polynomial function P and its graph are given.... Ch. Let us look at the graph of polynomial functions with different degrees. We can enter the polynomial into the Function Grapher, and then zoom in to find where it crosses the x-axis. 3 - The strength S of a wooden beam of width x and... Ch. P(x)=x33x2+3x2, Ch. A polynomial function of $$n^\text{th}$$ degree is the product of $$n$$ factors, so it will have at most $$n$$ roots or zeros, or $$x$$-intercepts. 3.7 - If the rational function y = r(x) has the... Ch. Let’s start off with the graph of couple of polynomials. Check whether it is possible to rewrite the function in factored form to find the zeros. A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed. 3.6 - Find all zeros of the polynomial. 3 - Find the quotient and remainder. 3.6 - So far, we have worked only with polynomials that... Ch. 3.2 - Market Research A market analyst working for a... Ch. A second-degree polynomial function in which all the coefficients of the terms with a degree less than 2 are zeros is called a quadratic function. 3 - A polynomial function P is given. 3 - Use the Factor Theorem to show that x+4 is a... Ch. Wait! Polynomials of degree greater than 2: Polynomials of degree greater than 2 can have more than one max or min value. The graph has 4 turning points, so the lowest degree it can have is degree which is 1 more than the number of turning points 5. Use the... Ch. 3 - Use a graphing device to graph the polynomial.... Ch. (a) Use a graphing... Ch. Check out some of my more of my videos:Calculus Playlist:https://www.youtube.com/playlist?list=PL5vENG_g67aHTpcVZWHHREIqa4fAcB0B495% Confidence Interval:https://www.youtube.com/edit?o=U\u0026video_id=CAZmr0kx2WQNewton Egg Drop Fail:https://www.youtube.com/edit?o=U\u0026video_id=s_t1hE89kS8Finding a relation from a table:https://www.youtube.com/edit?o=U\u0026video_id=1Ww6U__uy6ATrigonometric Proofs:https://www.youtube.com/edit?o=U\u0026video_id=HzmbCGcVWEIAbsolute Value Limits:https://www.youtube.com/edit?o=U\u0026video_id=uAGw21BtkSYInverse of a Quadratic Function:https://www.youtube.com/edit?o=U\u0026video_id=8wBwMpCPgyE Degree 4. 3.6 - Find all zeros of the polynomial. The degree of the polynomial is the highest degree of any of the terms; in this case, it is 7. I make video tutorials on pre-calculus 10, 11, and 12, trigonometry, calculus, Physics, circle geometry, and more. 3.2 - Graph the polynomial in the given viewing... Ch. 3 - Use a graphing device to analyze the graph of the... Ch. State... Ch. Graph: A horizontal line in the graph given below represents that the output of the function is … 3 - A stone is thrown upward from the top of a... Ch. The more corn a... Ch. Checking each term: 4z 3 has a degree of 3 (z has an exponent of 3) 5y 2 z 2 has a degree of 4 (y has an exponent of 2, z has 2, and 2+2=4) 2yz has a degree of 2 (y has an exponent of 1, z has 1, and 1+1=2) The largest degree of those is 4, so the polynomial has a degree of 4 3.5 - Evaluate the expression and write the result in... Ch. 3.2 - Graphs of Large Powers Graph the functions... Ch. Properties The graph of a second-degree polynomial function has its vertex at the origin of the Cartesian plane. P(x)=x3x6, Ch. 3.2 - Only one of the following graphs could be the... Ch. 3.6 - A polynomial P is given. The definition can be derived from the definition of a polynomial equation. Although it may seem daunting, graphing polynomials is a pretty straightforward process. 3.1 - Revenue A manufacturer finds that the revenue... Ch. Find the real zeros of the function. From... Ch. 3.3 - Use synthetic division and the Remainder Theorem... Ch. 3.5 - For the complex number 3+4i the real part is... Ch. A polynomial function is a function that can be expressed in the form of a polynomial. Recognizing Polynomial Functions. To find a polynomial of degree 4 that has the given zeros shown in the graph. 3.6 - Find all zeros of the polynomial. This isn't supposed to be about running? Figure 4: Graph of a third degree polynomial, one intercpet. But, you can think of a graph much like a runner would think of the terrain on a long cross-country race. 3.1 - Agriculture At a certain vineyard it is found that... Ch. 3 - Prove that the equation 3x4+5x2+2=0 has no real... Ch. Answers to Above Questions. The graph touches and "bounces off" the x-axis at (-6,0) and (5,0), so x=-6 and x=5 are zeros of even multiplicity. Therefore, The polynomial of degree 4 that has the given zeros as shown in the graph is. The degree of a polynomial function helps us to determine the number of $$x$$-intercepts and the number of turning points. Degree of a polynomial function is very important as it tells us about the behaviour of the function P(x) when x becomes v… Free polynomial equation calculator - Solve polynomials equations step-by-step This website uses cookies to ensure you get the best experience. In this case, the degree is 6, so the highest number of bumps the graph could have would be 6 – 1 = 5.But the graph, depending on the multiplicities of the zeroes, might have only 3 bumps or perhaps only 1 bump. I show you how to find the factors and the leading coefficient. 3.1 - Fencing a Horse Corral Carol has 2400 ft of... Ch. Ch. (I would add 1 or 3 or 5, etc, if I were going from … 3.6 - Find all zeros of the polynomial.... Ch. 3 - Find all real and complex zeros of P(x) = x3 x2 ... Ch. 3 - State the Remainder Theorem. 3 - Find the complete factorization of P(x) = x4 2x3... Ch. 3.2 - The graph of a polynomial function is given. 3 - Express the quadratic function f(x) = x2 x 6 in... Ch. x3+2x210x+3, Ch. 3 - What is the remainder when the polynomial... Ch. 2x4+3x312x+4, Ch. 3 - The profit P (in dollars) generated by selling x... Ch. 3 - Consider the following rational functions:... Ch. To graph polynomial functions, find the zeros and their multiplicities, determine the end behavior, and ensure that the final graph has at most turning points. Every real zero of a polynomial function appears as a/an _____ of the graph. Which of the graphs in Figure 2 represents a polynomial … 3 - Graph the polynomial by transforming an... Ch. 3 - Find the quotient and remainder. Another way to find the x-intercepts of a polynomial function is to graph the function and identify the points where the graph crosses the x-axis. 3.1 - The graph of f(x) = -3(x - 2)2 - 6 is a parabola... Ch. 3.7 - Transformations of y=1/x2 In Example 2 we saw that... Ch. 3.1 - A quadratic function is given. How we identify the equation of a polynomial function when we are given the intercepts of its graph? 3.7 - The Doppler Effect As a train moves toward an... Ch. I’ve has been a high-school mathematics teachers for 10 years. 3 - A quadratic function is given. 3.5 - Evaluate the radical expression and express the... Ch. 3.6 - Find all zeros of the polynomial. 3.6 - Roots of Unity There are two square roots of 1,... Ch. To answer this question, the important things for me to consider are the sign and the degree of the leading term. 3 - A polynomial function P is given. Ch. 3.7 - Constructing a Rational Function from Its... Ch. 3.2 - Determine the end behavior of P. Compare the... Ch. To find polynomial equations from a graph, we first identify the x-intercepts so that we can determine the factors of the polynomial function. Precalculus: Mathematics for Calculus - 6th Edition, Find the polynomial of the specified degree whose graph is shown. 3 - Height of a Baseball A baseball is thrown upward,... Ch. Degrees of a Polynomial Function “Degrees of a polynomial” refers to the highest degree of each term. 3.7 - Find the slant asymptote, the vertical asymptotes,... Ch. 3.1 - The graph of a quadratic function f is given. 3.7 - Graph the rational function, and find all vertical... Ch. See . 3.4 - Find integers that are upper and lower bounds for... Ch. 3.2 - Possible Number of Local Extrema Is it possible... Ch. Find the multiplicity of a zero and know if the graph crosses the x-axis at the zero or touches the x-axis and turns around at the zero. 3.1 - Agriculture The number of apples produced by each... Ch. 3 - Find the quotient and remainder. 3 - What is meant by a local maximum point or local... Ch. 3.3 - Nested Form of a Polynomial Expand Q to prove that... Ch. x48x2+2x+7x+5, Ch. Once you have found the zeros for a polynomial, you can follow a few simple steps to graph it. P(x)=x37x2+17x15, Ch. 2 . Plus, you’ll have access to millions of step-by-step textbook answers! (a) Express the... Ch. x2+x12x3, Ch. The exponent says that this is a degree-4 polynomial; 4 is even, so the graph will behave roughly like a quadratic; namely, its graph will either be up on both ends or else be down on both ends.Since the sign on the leading coefficient is negative, the graph will be down on … 3.6 - If the polynomial function P has real coefficients... Ch. 3.1 - To put the quadratic function f(x)=ax2+bx+c in... Ch. •recognise when a rule describes a polynomial function, and write down the degree of the polynomial, •recognize the typical shapes of the graphs of polynomials, of degree up to 4, •understand what is meant by the multiplicity of a root of a polynomial, •sketch the graph of a polynomial, given its expression as a product of linear factors. 3 - A polynomial P is given. 3 - Perform the indicated operation and write the... Ch. 3.4 - Possible Rational Zeros List all possible rational... Ch. 3.3 - Show that the given value(s) of c are zeros of... Ch. 3.1 - 233-42 Find the maximum or minimum value of the... Ch. 3.4 - Use Descartes Rule of Signs to determine how many... Ch. 3 - What is a complex number? 3.6 - A polynomial P is given. 3.3 - If we divide the polynomial P by the factor x c... Ch. 3.7 - Find the x- and y-intercepts of the rational... Ch. 3 - Does there exist a polynomial of degree 4 with... Ch. 3.1 - Pharmaceuticals When a certain drug is taken... Ch. 3.5 - If 3+4i is a solution of a quadratic equation with... Ch. 3.4 - Possible Rational Zeros A polynomial function P... Ch. Hello and welcome to this lesson on how to mentally prepare for your cross-country run. 3.4 - True or False? 3 - Let P(x) = 2x3 5x2 4x + 3. Ch. To graph polynomial functions, find the zeros and their multiplicities, determine the end behavior, and ensure that the final graph has at most $$n−1$$ turning points. Zero Polynomial Functions Graph. Example. 3.6 - Find all zeros of the polynomial. 1. 3.3 - Find the quotient and remainder using long... Ch. The highest power of the variable of P(x)is known as its degree. 3.2 - Volume of a Box An open box is to be constructed... Ch. 3.1 - Vertex and x-Intercepts We know that the graph of... Ch. By factor theorem, x−(−2),x−(−2),x−1,x−1 should be factors of the desired polynomial. 3.3 - Impossible Division? Note: Ignore coefficients -- coefficients have nothing to do with the degree of a … 3.2 - Maximum Number of Local Extrema What is the... Ch. The graphs of several second degree polynomials are shown along with questions and answers at the bottom of the page.. Polynomial of a second degree polynomial: touches the x axis and upward. It is a linear combination of monomials. (a) Find all real zeros... Ch. I have videos on: slope, lines, quadratics, exponents, circles, tangents, derivatives, limits, solving equations, and many more. Find all the... Ch. 3.2 - Graph the function P(x)=(x1)(x3)(x4) and find all... Ch. P(x)=x4x2+2x+2. What? 3.6 - Find all zeros of the polynomial. 3.1 - The quadratic function f(x) = a(x - h)2 + k is in... Ch. 3.7 - Find the intercepts and asymptotes, and then... Ch. 3.1 - Use the formulas of this section to give an... Ch. 3.7 - Find all horizontal and vertical asymptotes (if... Ch. Graphing a polynomial function helps to estimate local and global extremas. 3.3 - Use the Factor Theorem to show that xc is a factor... Ch. (a) List all possible... Ch. Graphing a polynomial function helps to estimate local and global extremas. See . Steps involved in graphing polynomial functions: 1 . 3.7 - A rational function is given. To find the degree all that you have to do is find the largest exponent in the polynomial. 3.1 - Find the domain and range of the function.... Ch. 3 - Use a graphing device to find all real solutions... Ch. Remember that the degree of the polynomial is the highest exponentof one of the terms (add exponents if there are more than one variable in that term). To find a polynomial of degree 4 that has the given zeros shown in the graph. 3.6 - (a) If a is a zero of the polynomial P, then... Ch. So it has degree 5. 3.3 - Two polynomials P and D are given. (a)... Ch. 3.7 - Use transformations of the graph of y=1x to graph... Ch. Question 1: Why does the parabola open upward? Use the Leading Coefficient Test to find the end behavior of the graph of a given polynomial function. Ask subject matter experts 30 homework questions each month. 3.2 - Impossible Situation? 3+4i3+4i=. 3 - Find the quotient and remainder. 3 - What is the remainder when x101x4+2 is divided by... Ch. 3 - How does synthetic division work? 3 - Tire Inflation and Treadwear Car tires need to be... Ch. n is a positive integer, called the degree of the polynomial. Khan Academy is a 501(c)(3) nonprofit organization. 3 - What does it mean to say that a is a lower bound... Ch. 3.4 - Show that the given values for a and b are lower... Ch. P(x)=x42x32x22x3. Finding the equation of a Polynomial from a graph by writing out the factors. 3.4 - A polynomial P is given. 3 - State the Rational Zeros Theorem. 3.7 - A Rational Function with No Asymptote Explain how... Ch. The polynomial of degree 4 that has the given zeros as shown in the graph is, The zeros are given in the graph as −2,−2,1,1. 3.1 - Find the maximum or minimum value of the function.... Ch. 3.7 - Flight of a Rocket Suppose a rocket is fired... Ch. 3.1 - A quadratic function is given. By using factor theorem, x−c is a factor of P(x) ; when c is a zero of P . 3.7 - Drug Concentration A drug is administered to a... Ch. 3.5 - Complex Conjugate Roots Suppose that the equation... Ch. 3.7 - If the rational function y = r(x) has the vertical... Ch. Why does the graph of this polynomial have one x intercept only? Oh, that's right, this is Understanding Basic Polynomial Graphs. 3.2 - Recall that a function f is odd if f(x)=f(x) or... Ch. See and . Suppose you were asked to... Ch. 3.7 - Population Growth Suppose that the rabbit... Ch. Ch. Graphing is a good way to find approximate answers, and we may also get lucky and discover an exact answer. 3.1 - Path of a Ball A ball is thrown across a playing... Ch. 3.2 - How many x -intercepts and how many local extrema... Ch. Ch. 3.5 - Find the real and imaginary parts of the complex... Ch. 3.3 - Find the polynomial of the specified degree whose... Ch. 3 - Find the maximum or minimum value of the quadratic... Ch. Ch. Even-degree polynomial functions have graphs with the same behavior at each end. : P ( x ) = 2x3 5x2 4x + 3 a given function! And 12, trigonometry, Calculus, Physics, circle geometry, and degrees. More than one max or min value uses cookies to ensure you get the best.. Of a polynomial with integer coefficients that... Ch function from its... Ch, 11, and,. Polynomial using... Ch using factor Theorem to Show that xc is a polynomial of the graph of a function. Equation... Ch Let ’ s start off with the graph of the equation... 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