Answered


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

minimum point for the function. Explain your answer.

BRewrite f(x) in vertex form by completing the square.

Verified Answer :

ashisthebest1

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:

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

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