Question

A soccer ball is kicked into the air. its height is approximated by the equation h(t)= -5t^2+45t, where h is the height in meters and t is the time is seconds.

A.)What are the X-intercepts? When does the soccer ball hit the ground?

B.)What are the coordinates of the vertex? What is the max height of the soccer ball? How long does it take to hit it's max height?

Answer 1

-5T^2 + 45t
to find the x intercepts equate to 0 and silve for t
-5t^2 + 45t= 0
-5t(t - 9) = 0
t = 0 and 9 These are the x intercepts

the vertex can be found by converting the function to vertex form

(ht) = -5(t^2 - 9t)
= -5[ (t - 4.5t)^2 - 20.25]

so the coordinates of the vertex are t = 4.5 and h(t) = -5 * -20.25 = 101.25
( 4.5 , 101.25)
The maximum height is 101.25 m and time it takes to reach this height is 4.5 seconds.