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1 Math 60 Ch3 practice Test The graph of f(x) = 3(x 5) + 3 is with its vertex at ( maximum/minimum value is ( ). ) and the The graph of a quadratic function f(x) = x + x 1 is with its vertex at ( the maximum/minimum value is ( ). ) and 1 The graph of a quadratic function f x x x is with its vertex at ( ) and the maximum/minimum value is ( ). For a quadratic function is given f(x) = 3x + 6x, (a) Express the quadratic function in standard form. (b) Find its vertex (c) x- and y-intercept(s). (If an answer does not exist, enter DNE.) For a quadratic function is given f(x) = x + x + 6 (a) Express the quadratic function in standard form. (b) Find its vertex (c) x- and y-intercept(s). (If an answer does not exist, enter DNE.) For a quadratic function is given f(x) = x 3x + 3 (a)express the quadratic function in standard form. (b) Find its vertex (c)x- and y-intercept(s). (If an answer does not exist, enter DNE.) A quadratic function is given h(x) = 1 x x f(x) = x + x + 1 f(x) = 3 + 3x x f(x) = 3 + 3x x h(x) = f(x) = 1 4 x x x x x f(x) = 9 x (a) Express the quadratic function in standard form. (b) Sketch its graph. Find the maximum or minimum value of the function, g(x) = x(x 4) + 7 Find a function whose graph is a parabola with vertex (5, ) and that passes through the point (4, 1).

Find the domain and range of the function. (Enter your answers using interval notation.) f(x) = x + 16x 63 domain range Find the domain and range of the function.

2 Find the domain and range of the function. (Enter your answers using interval notation.) f(x) = x + 16x 63 domain range Find the domain and range of the function. (Enter your answers using interval notation.) f(x) = x + 16x 63 domain range A rain gutter is formed by bending up the sides of a 44-inch-wide rectangular metal sheet as shown in the figure. (a) Find a function that models the cross-sectional area of the gutter in terms of x. (b) Find the value of x that maximizes the cross-sectional area of the gutter. (c) What is the maximum cross-sectional area for the gutter? A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 x, as shown in the figure. Each piece is bent into the shape of a square. (a) Find a function that models the total area enclosed by the two squares. (b) Find the value of x that minimizes the total area of the two squares. Factor the polynomial and use the factored form to find the zeros and Sketch the graph. P(x) = x 3 + x 4x 8 P(x) = x 3 x 18x + 9 P(x) = x 4 3x 3 + 7x 81 P(x) = x 4 8x 9

Determine the end behavior of P(x) = y ( ) as x, y ( ) as x 1 3 18 x x x Determine the end behavior of P(x) = x 11 3x 9 y ( ) as x, y ( ) as x Sketch the graph of a polynomial function 1 4 px x x 9 9

3 Determine the end behavior of P(x) = y ( ) as x, y ( ) as x x x x Determine the end behavior of P(x) = x 11 3x 9 y ( ) as x, y ( ) as x Sketch the graph of a polynomial function 1 4 px x x An open box is to be constructed from a piece of cardboard 30 cm by 60 cmlength x from each corner and folding up the sides, as shown in the figure. (a) Express the volume V of the box as a function of x. (b) What is the domain of V? If we divide the polynomial P by the factor x c and we obtain the equation P(x) = (x c)q(x) + R(x), then we say that x c is the divisor, Q(x) is the ( ), and R(x) is the ( ) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) Q(x) + R(x). P(x) = 4x + 5x 3, D(x) = x + 4 P(x) = x 4 x 3 + 9x + 3, D(x) = x + 8 P(x) = 10x 3 + x 1x + 9, D(x) = 5x 7 Find the quotient and remainder using long division. x 3 + 4x + x 8x + 6x 3 + x + 6x x + 5

4 x 6 3x 4 + x 3 x 3 x 3 + 7x 4x + 8 x 1/ x 3 64 x 4 Find a polynomial of the specified degree that has the given zeros: Degree 3; zeros : 4, 4, 6 Find a polynomial of degree 3 that has zeros 1, 4, and 5 and in which the coefficient of x is 3. Find a polynomial of degree 4 that has integer coefficients and zeros 3, 3, 4, and ½. Find the polynomial of the specified degree whose graph is shown. Degree 3 Find the polynomial of the specified degree whose graph is shown. Degree 4

5 Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list.) Write the polynomial in factored form and graph them. P(x) = x 3 6x + 3x P(x) = x 4 13x + 36 P(x) = 3x 4 10x 3 9x + 40x 1 P(x) = 6x x 3x P(x) = x 3 + 1x + 14x 4 P(x) = x 4 4x 3 0x 9x + 14 P(x) = x x x + 8x P(x) = x 4 5x 3 + 6x + 4x 8 Use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the polynomial can have. Then determine the possible total number of real zeros. number of positive zeros possible, number of negative zeros possible number of real zeros possible P(x) = x 3 x x 4, P(x) = 4x 3 7x + 9x 4, Evaluate the expression i 10 Evaluate the expression and write the result in the form a + bi. (Simplify your answer.) 4 i 7 7i Find all solutions of the equation and express them in the form a + bi. 3 t 3 0 t Factor the polynomial completely: P(x) = x x 16 Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 4 and 1 + i. Find all zeros of the polynomial. P(x) = x 3 10x 4 A polynomial P is given P(x) = x 6 64 (a) Factor P into linear and irreducible quadratic factors with real coefficients. (b) Factor P completely into linear factors with complex coefficients.

6 Find all horizontal and vertical asymptotes (if any). vertical asymptote : x = s x 16x 1 4x x 6 horizontal asymptote : y = (c) (d) Find the intercepts and asymptotes. (If an answer does not exist, enter DNE.) r x 8x 8 x, rx x 5 x 1 r x, x x 4 4x 1 x-intercept y-intercept vertical asymptote horizontal asymptote

x 2 + 6x 18 x + 2 Name: Class: Date: 1. Find the coordinates of the local extreme of the function y = x 2 4 x.

x 2 + 6x 18 x + 2 Name: Class: Date: 1. Find the coordinates of the local extreme of the function y = x 2 4 x. 1. Find the coordinates of the local extreme of the function y = x 2 4 x. 2. How many local maxima and minima does the polynomial y = 8 x 2 + 7 x + 7 have? 3. How many local maxima and minima does the