Question

you throw a ball up in the air. given the function
h=-16t^2+20t+6

1)when does the ball reach it maximum height? and

2)what is the ball's maximum height?

Answer 1

your equation
h= -16t^2+20t+6

is modelled by a parabola which opens downwards.

Find the vertex of this parabola by the means that you learned, and you will have both answers.

Answer 2

I assume you are not a calculus student.

This is a parabola. Looking at the zeroes
0=-16t^2+20t+6
( 8t+2)(-2t+3)=0
t=-1/4, t=3/2
because the maximum will occure at the halfway point between two zeroes, then
half way: (1.5+.25)/2 - 1.5
=1.5-(1.75)/2=

t=.625 is the location of the max

for max height, plug that t into the original equation.