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.
I tried to do this question on a test but I just ran out of time
How is the easiest and quickest way to do this?

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

Answer 1

Of course you would want to find the vertex of the hyperbola

several easy ways to do this
1. for the general quadratic y = ax^2 + bx + c
the x of the vertex is -b/(2a), then plug that back into the equation to find the y

so here , t of the vertex = -21/-10 = 2.1
then H = -5(2.1)^2 + 21(2.1) = 22.08

2. in any parabola, the x of the vertex is always midway between the x-intercepts, if they exist
so for yours 0 = -t(5t - 21)
t = 0 or t = 21/5
half-way would be t = 21/10 = 2.1
continue as in #1

3. complete the square