Grade 10 Math Question

Question

A football is punted. Its height, H metres is given by the quadratic relation with equation: H = -5t² + 21t, where t is the time in seconds after the punt. 

Algebraically determine the maximum height of the football. Show all of your steps.

Answer 1

The maximum is when the derivative or slope is equal to 0. The derivative is -10t + 21.

So, -10t + 21 = 0

-10t = -21

t = 21/10 or 2.1 seconds

Or in algebra, this is the same as -b/2a to find the x coordinate of the vertex. -21/2(-5) = 21/10 seconds

Now plug 2.1 into the original equation to solve for the y-coordinate (H) and this will be your height at the vertex/maximum:

Y = -5(2.1)^2 + 21(2.1)