# Math Help - A quadratic function problem

1. ## A quadratic function problem

Can someone please solve or tell me how i would do this question. I'm finding it really difficult.

A projectile is launched from the top of a building. The height (h meters) of the projectile above the ground is given by the equation h=15 + 20t - 2t^2 where t is the time of flight in seconds.

(a) sketch the graph to represent the flight
(b) What is the greatest height reached?
(c) What is the height of the building?
(d) After what time did the projectile strike the ground?

2. $h = -2t^2 + 20t + 15$

(b) Change a quadratic equation to vertex form by completing the square:
$h = -2t^2 + 20t + 15$
$h = -2(t^2 - 10t) + 15$
$h = -2(t^2 - 10t + 25 - 25) + 15$
$h = -2(t^2 - 10t + 25) + 50 + 15$
$h = -2(t - 5)^2 + 65$
The vertex is (5, 65), and this is the maximum point of the parabola. So the greatest height is 65 feet.

(c) Since the projectile started at t = 0 from the top of the building, plug in 0 for t into the equation and simplify.

(d) When the projectile hits the ground, h = 0. So plug in 0 for h into the equation and solve for t.