Question

A) Given the function f(x) = -x^2 + 8x + 9, state whether the vertex represents a maximum or

minimum point for the function. Explain your answer.
b) Rewrite f(x) in vertex form by completing the square.

Answer 1

find the vertex using vertex formula
-b ÷ 2a -8 ÷ -2 x = 4 for y plug in
F(x) = -(4)² + 8(4) + 9
= -16 + 28 +9
= 12 + 9
= 21
(4,21)
vertex form
y = -(x - 4)² + 21
so that means it will flip down - means flip down
so vertex represents a maximum point

Answer 2

the vertex represents a maximum

Vertex is (4,7)

f(x)=-(x-4)^2+7

Explanation:

Given the function
`f(x) = -x^2 + 8x + 9`

Equation is in the form of y=ax^2+bx+c

`a=-1`

When 'a' is negative, then vertex is maximum

when 'a' is positive, then vertex is minimum

`a=-1` is negative, so the vertex represents a maximum

`f(x) = -x^2 + 8x + 9`, factor out negative

Take out negative sign in common