Question

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

Answer 1

Answer:

the vertex represents a maximum

Vertex is (4,7)

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

Step-by-step 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

Answer 2

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