A quadratic function f is given. f(x) = - 16x2+ 40x + 11 (a) Determine whether the given quadratic function has a maximum value or a minimum value. Then find 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 fill in the answer box to complete your choice. (Simplify your answer.) O A. The function f has a minimum value of O B. The function f has a maximum 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 (3, - 14) and y-intercept 22. f(x) = (Use integers or decimals for any numbers in the expression.)For the given polynomial function fcomplete parts (a) through (9). x) :(x72)2(x+ 3W4) to) Describe the end behavior of f. Choose the correct answer below. 0 A. The graph rises to the left and to the right. 0 B. The graph rises to the teft and falls to the right. 0 C. The graph falls to the left and rises to the right. 0 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 x-intercept. Select the correct choice betow and, if necessary, tilt in the answer box to complete your choace. O A- The realzeros offare . (Type an integer or a simplied fraction. Type each solution only once. Use a comma to separate answers as needed.) O B. The function f has no real zeros. What is graph's behavior at the smallest x-intercept? Choose the correct answer below. 0 The graph crosses the xeaxis. O The graph touches but does not cross the x-axis. O The function f has no real zeros. What l5 the graph's behavior at the next smallest xintercept? Choose the correct answer below 0 The graph touches but does not cross the x-axis. O The graph crosses the xaxis. O The function f has no real zeros. What is the oranh's behavior at the other xiintercent'i Choose the correct answer below For the given polynomial function fcomplete parts (a) through (9). ftX) :lxi2)2(x+ 3ltxi4) What is the graph's behavror at the other xintercept? Choose the correct answer below. O The graph touches but does not cross the x-axis. O The graph crosses the xaxis. O The function f has no real zeros. (c) Use the zeros of f and test numbers to nd the intervals over which the graph of f is above or below the xaxis Select the correct choice below and, it necessary, nil in the answer box to complete your choice. O A- The graph of f is above the xeaxis on the lnterval (Type your answer in interval notation.) O B. The graph of f is not above the xeaxis. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. O A- The graph of t is below the x-axis on the interval (Type your answer in interval notation.) O B. The graph of t is not below the x-axis (d) Determine the yeintercept. The yeintercept is . (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 yaxis symmetry Thn nrunh in\" nrinin \".mmnin. For the given polynomial function f complete parts (a) through (9). f ( x ) = (x - 2)2 (x + 3)(x -4) U A. The graph of f is below the x-axis on the interval (Type your answer in interval notation.) O B. The graph of f is not below the x-axis. (d) Determine the y-intercept. The y-intercept is (Simplify your answer. Type an integer or a fraction.) (e) Find any symmetries of the graph of the function. Choose the correct answer below. O The graph has y-axis symmetry. O The graph has origin symmetry. O The graph has no symmetries. (f) Determine the maximum possible number of turning points. The maximum possible number of turning points is. (Type a whole number.) (g) Sketch the graph of f. Choose the correct graph below. O A. O B. O C. OD. Ay 60- 100- 48- X 10 10 10 -196- -2003 -2603Divide using long division. State the quotient, q(x), and the remainder, r(x). 5x3 -6x2 + 5x + 8 5 x2 + 4x + 2 5x3 - 6x2 + 5x + 8 5x2 + 4x + 2 0+ 5 x2 + 4x + 2 (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.)Use synthetic division to find the quotient and the remainder. 7v3 + 20v2 + 8v-14 v + 2 The quotient is (Use integers or fractions for any numbers in the expression. Do not factor.) The remainder is (Type an integer or a simplified fraction.)Find all rational zeros of the given polynomial function, f(x):x372x2713x710 Select the correct choice below and, if necessary, ll in the answer box to complete your choice. 0 A- The set of rational zeros of f(x) is D. (Type an integer or 3 Simplied fraction, Use a comma to separate answers as needed) 0 B. The given function has no rational zeros Find all rational zeros of f. Then (if necessary) use the depressed equation to find all roots of the equation f(x) = 0. 9x 3 - 12x2 - 8x - 1=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { } (Type an exact answer, using radical as needed. Type an integer or a fraction. Use a comma to separate answers as needed.) O B. There are no real zeros.Find a polynomial P(x) with real coefficients having a degree 4, leading coefficient 4, and zeros 2 - i and 4i. P(x) = (Simplify your answer.)Find the oblique asymptote of the graph of the rational function and sketch the graph the rational iunc'ion, x27x76 tap? a. Find the 0b ique asymptote of the graph of f. Seiect the correct choice below and ll in any answer boxes within your choice. 0A. 5,: O B. There is no oblique asymptote. Sketch the graph the rational function Choose the correct graph below, 03- Oc. ..3 p .p. Suppose q is directly proportional to the square root of h and inversely proportional to the cube of j, q= and q = 12 when h = 16 and j = 2. Find q when h = 9 and j = 3