Question

A ball is launched from a slingshot. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.

After 1 second, the ball is 148 feet in the air, after 2 seconds the ball is 272 feet in the air.

Find the height in feet of the ball after 6 seconds in the air?

Answer 1

I guess it starts at 0 height

h = a x^2 + b x

148 = a (1)^2 + b(1)
272 = a(2)^2 + b(2)

b = 148 - a

272 = 4 a + 2 (148-a)
272 = 4 a -2 a + 296
2 a = -24
a = -12 (should be 16 on earth but anyway)

b = 148 +12 = 160
so

h = -12 x^2 + 160 x

if x = 6
h = -12*36 + 160(6) = 528