A Longhorn kicker recently kicked a 54-yard field goal during practice. The football started at a height of 0 ft, and the football was 12 ft off the ground when it made it a horizontal distance of 54 yards. Assume that the football hits the ground 10 yards after it passes the goal post. What was the maximum height of the football? Round to the nearest whole number in FEET.

23 feet

Vertex form: y=a(x-h)^2+k

we will draw a graph and have 3 points( 0,0), (54,12) and (64,0)

Then convert yard to feet, (0,0),(162) and (192,0)

0=a(0-96)^2+k

a= -k/9216

then

0=a(0-96)^2+k

12=-k/9216(162-96)^2+k

k=22.755 round it to 23

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3