Question

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

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

A. −16x2 + 24x + 16 = 0

-8(2x2 - 3x - 2) = 0

-8(2x + 1 )(x - 2) = 0

x = -0.5, 2.

So the x-intercepts are (-0/5, 0) and (2, 0).

B.  As the leading coefficients is negative (-16) the vertex of the graph will be a Maximum.

To find its coordinates we convert the function to vertex form:

f(x) =  −16x2 + 24x + 16

=  -16(x^2 - 1.5x) + 16

Completing the square on  contents of the parentheses:

= -16 [(x - 0.75)^2  - 0.75^2] + 16

= -16(x - 0.75)^2  - 16 * -0.75^2 + 16

= -16(x - 0.75)^2 + 9 + 16

= -16(x - 0.75)^2 + 25.

So the coordinates of the vertex are (0.75, 25)