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

Answer:

The correct option is C.

Step-by-step 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.