a ball is thrown vertically upward from the top of a cliff. the height of the ball is modelled by the function h(t) = 65 + 10t - 5t^2, where h(t) is the height in metres and t is the time in seconds. determine when the ball will reach its max height

Question

anonymous · Answer

To solve for the vertex (peak of arc):
-b
---
2a

This will give you the time at peak, if you need to know the peak value, plug that answer into x in the original problem and solve for y, or peak elevation of arc.

anonymous · Answer

@hpilato

anonymous · Answer

well im supposed to factor the equation.. so i would have   -5(-13-5t+t^2)... but im stuck there

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

there's no need to factor

use ehuman's method

jim_thompson5910 · Answer

use the formula t = -b/(2a)

in this case, a = -5 and b = 10

t = -b/(2a)

t = -10/(2*(-5))

t = -10/(-10)

t = 1

So it will take 1 second for the ball to reach the max height.

anonymous · Answer

ok! thank you both so much, i wouldnt have known to do that! :)

anonymous · Answer

it is derived from the quadratic formula, and gives the x value of the vertex.