Question

PLS HELP ME WITH THIS I HAVE BEEN STUCK FOR OVER AN HOUR

Use the function f(x) to answer the questions.

f(x) = −16x2 + 24x + 16

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Answer 1

Answer:coesm

Explanation:

Answer 2

See Explanation

Explanation:

A. f(x) = -16x² +24x + 16

0 = -8(2x² - 3x - 2) ⇒ -8(2x + 1)(x - 2) = 0 ⇒ x = -1/2, 2

B. f'(x) = -32x + 24 ⇒ 0 = -8(4x - 3) ⇒ x = 3/4

f''(x) = -32 ⇒ f''(3/4) = -32 ⇒ concave down ⇒ maximum

f(3/4) = -16(9/16) + 24(3/4) + 16 = -9 + 18 + 16 = 25

By the second derivative test, the point (3/4, 25) is a maximum.

C. 1. Plot the intercepts. 2. Plug in points. 3. Draw the curve.