Select the quadratic function with a graph that has the following features
x-intercept at (8,0)
y-intercept at (0,-32)
maximum value at (6,4)
axis of symmetry at x=6
a. f() = 1/2 x2 +6 - 32
b. f() = -x2 + 12x -32
c. f() = 1/2 x2 + 6x -16
d f() = -x2 + 12x -6

Option B

Step-by-step explanation:

we know that

For the given values, the quadratic function is a vertical parabola open downward (vertex is a maximum)

The equation in vertex form is equal to

where

(h,k) is the vertex

a is a coefficient

we have

(h,k)=(6,4)

so

Find the value of a

For x=8, y=0 -----> the y-intercept

substitute

substitute

Convert to standard form

The graph in the attached figure