Question

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(x)= -1/2x^2+6x-32
B. f(x)= -1/2x^2+6x-16
C. f(x)-x^2+12x-32
D. f(x)= -x^2+12x-36

Answer 1

C.

Explanation:

I took the test and it was right

Answer 2

The correct option is C.

Explanation:

The function has axis of symmetry at
`x=6`, it represents that the parabola is along the x-axis and the standard form of parabola is

`y=a(x-h)^2+k`

Where, a is scale factor and (h,k) is vertex.

The maximum or minimum value of a quadratic function is the vertex of parabola. So, vertex of parabola is (6,4).

`y=a(x-6)^2+4`

The y-intercept of the function is (0,-32)

`-32=a(0-6)^2+4`

`-32-4=36a`

`-36=36a`

`a=-1`

Therefore required equation of parabola is

`y=-(x-6)^2+4`

`y=-(x^2-12x+36)+4`

`y=-x^2+12x-36+4`

`y=-x^2+12x-32`

Therefore option C is correct.