Daph044
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The graph of a quadratic function has a vertex located at (7,-3) and passes through points (5,5) and (9,5). Which equation best represents this function?
A) f(x)=(x-7)^2-3
B) f(x)=2(x-7)^2-3
C) f(x)= -(x-5)^2+5
D) f(x)= -2(x-5)^2+5

Respuesta :

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Answer:

B) [tex]f(x)=2(x-7)^2-3[/tex].

Step-by-step explanation:

The vertex form of the equation is given by [tex]f(x)=a(x-h)^2+k[/tex].

We plug in the vertex to obtain:

[tex]f(x)=a(x-7)^2-3[/tex].

Since the graph passes through (5,5) and (9,5), they must satisfy its equation.

[tex]5=a(9-7)^2-3[/tex].

[tex]5+3=4a[/tex].

[tex]8=4a[/tex]

Divide both sides by 4.

[tex]a=2[/tex]

Therefore the equation is:

[tex]f(x)=2(x-7)^2-3[/tex].

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