contestada


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.

Respuesta :

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 [tex]f(x) = -x^2 + 8x + 9[/tex]

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

[tex]a=-1[/tex]

When 'a' is negative, then vertex is maximum

when 'a' is positive, then vertex is minimum

[tex]a=-1[/tex] is negative, so the vertex represents a maximum

[tex]f(x) = -x^2 + 8x + 9[/tex], factor out negative

Take out negative sign in common

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