Question

George kicked a ball while standing at the top of a hill.

The trajectory of the ball follows the equation
y
=
−
16
x
2
+
32
x
+
12
.
The slope of the hill can be represented by the equation
y
=
−
4
x
+
12
.
What are the coordinates of the point of impact between the ball and the hill?


(
2.25
,
3
)


(
0
,
12
)


(
3
,
0
)


(
3
,
2.25
)

Answer 1

Set the equations equal:
-16x^2 + 32x + 12 = -4x + 12
→ -16x^2 + 36x = 0
→ -4x(4x - 9) = 0
so x = 0 or x = 9/4 = 2.25.

y at x = 2.25: y = -4(2.25) + 12 = 3.

x = 0 gives the starting point (0,12), so the impact point is (2.25, 3).