Question

Compare 𝑓⁡(𝑥)=−𝑥2+6⁢𝑥−15 to the quadratic function g(x) shown in the table. Which function has the greater maximum? 1 of 1.
Select Choice



x g(x)
−6 −26
−3 −11
0 −2
3 1
6 −2
what is the vertex of both?

Answer 1

f(x) = −x^2 + 6x − 15:
- a = −1, b = 6 so x-coordinate of vertex = −b/(2a) = −6/(2·−1) = 3.
- f(3) = −9 + 18 − 15 = −6.
- Vertex of f: (3, −6). This is the maximum of f.

g(x) from the table:
- Values are symmetric about x = 3 (g(0)=g(6)=−2), so the axis is x = 3 and the vertex is at x = 3.
- g(3) = 1, so vertex of g: (3, 1). (In fact g(x) = −(1/3)(x−3)^2 + 1.)

Comparison:
- Maximum of f is −6; maximum of g is 1. g(x) has the greater maximum (by 7).