Asked by Fred

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.

Answers

Reiny
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

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