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A quadratic function f is given. f(x) = 4x2 + 20x + e [a] Determine whether the given quadratic function has a maximum value or
A quadratic function f is given. f(x) = 4x2 + 20x + e [a] Determine whether the given quadratic function has a maximum value or a minimum value. Then nd this value. (b) Find the range of f. [a] Does the quadratic function f have a minimum value or a maximum value? Select the correct answer below and ll in the answer box to complete your choice. (Simplify your answer.) O A. The function f has a maximum vaiue of Q B. The function f has a minimum value of (b) The range of f is . (Type your answer in interval notation.) Find a quadratic function of the form f(x) = ax + bx + c that satisfies the following conditions. The graph of f has vertex (4, - 4) and y-intercept 76. . . . f(x) = (Use integers or decimals for any numbers in the expression.)For the given polynomial function f complete parts [a] through [9]. f(X)=(I-1)2(X+4)(X- 3) [3] Describe the end behavior of f. Choose the correct answer below. 0 A. The graph rises to the left and falls to the right. 0 B. The graph falls to the left and rises to the right. 0 C. The graph rises to the left and to the right O D. The graph falls to the left and to the right. (b) Find the real zeros of f. Determine whether the graph of f crosses or touches but does not cross the xaxis at each xintercept. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. O A- The real zeros of f are . (Type an integer or a s'mplied fraction. Type each solution only once. Use a comma to separate answers as needed.) O E. The function f has no real zeros. What is graph's behavior at the smallest xintercept'? Choose the correct answer below. O The graph touches but does not cross the xaxis. O The graph crosses the xaxis. O The function f has no real zeros. For the given polynomial function f complete parts [a] through [9]. ftX)=(I-1)2(X+4)(X- 3) What is the graph's behavror at the next smallest xintercept? Choose the correct answer below. 0 The graph touches but does not cross the xaxis. O The graph crosses the xaxis. O The function f has no real zeros. What is the graph's behavror at the other xintercept'? Choose the correct answer below. 0 The graph crosses the xaxis. O The graph touches but does not cross the xaxis. O The function f has no real zeros. [0) Use the zeros of f and test numbers to nd the intervals over which the graph off is above or below the xaxis. Select the correct choice below and, it necessary, ll in the answer box to complete your choice. O A- The graph off is above the xraxis on the interval (Type your answer in interval notation.) O B. The graph off is not above the xaxis. Select the conect choice below and. if necessary, ll in the answer box to complete your choice. For the given polynomial function f complete parts [a] through [9]. x) =(x1)2(x+4)(x 3) Select the correct choice below and, it necessary, ll in the answer box to complete your choice. O A- The graph off is below the xaxis on the interval (Type your answer in interval notation.) O B. The graph off is not below the xaxis. {d} Determine the ylntercept. The yintercept is (Simpiify your answer. Type an integer or a fraction.) (e) Find any symmetnes of the graph of the function. Choose the correct answer below. 0 The graph has no symmetries. O The graph has yaxis symmetry O The graph has origin symmetry. {f} Determine the maximum possible number of turning points. The maximum possible number of turning points is (Type a whole number.) For the given polynomial function f complete parts [a] through [9}. f(X) =(x1)2(x+4)(x 3) (Simplify your answer. Type an integer or a fraction.) (e) Find any symmetries of the graph of the function. Choose the correct answer below. 0 The graph has no symmetries. O The graph has yaxis symmetry O The graph has origin symmetry. (f) Determine the maximum possible number of turning points. The maximum possible number of turning points is (Type a whole number.) {9) Sketch the graph of f. Choose the correct graph below. OA. QB. 00. on. Divide using long division. State the quotient, q(x), and the remainder, r(x). 4x3 - 4x2 + 6x + 2 4x2 + 4x +4 -.. 4x3 - 4x2 + 6x + 2 4x2 + 4x + 4 4x2 + 4x + 4 (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.)
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