Jen is investigating a quadratic function g(x). She writes four different forms of the function, as shown below.

Question

Select the form that reveals the vertex of g(x) without having to be rewritten.(1 point)
Responses

g(x)=−2(x−6)(x−2)
g of x is equal to negative 2 open paren x minus 6 close paren open paren x minus 2 close paren

g(x)=−2(x2−8x+12)
g of x is equal to negative 2 times open paren x squared minus 8 x plus 12 close paren

g(x)=−2(x−4)2+8
g of x is equal to negative 2 times open paren x minus 4 close paren squared plus 8

g(x)=−2x2+16x−24
g of x is equal to negative 2 x squared plus 16 x minus 24

Answer 1

The form that reveals the vertex of \( g(x) \) without having to be rewritten is:

\[ g(x) = -2(x - 4)^2 + 8 \]

In this vertex form of a quadratic function \( g(x) = a(x - h)^2 + k \), the vertex is given by the point \( (h, k) \). In this case, the vertex is \( (4, 8) \).