The graph of h(x) = −3x^2 + 36x − 96 can be used to model the height in feet of a curved arch support for a flyover, where the x-axis represents the ground level and x represents the distance in feet at the ground level from one side of an arch support to the other. Find the height of the highest point of the flyover.

Choices:
A: 8 ft
B: 10 ft
C: 12 ft
D: 16 ft

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.