Question

A ball is shot upward such that its height (in feet) above the ground after t seconds is h(t) = -16t2 + 96t + 5. What is the ball's maximum height?​

Answer 1

149 feet

Explanation:

you have a quadratic equation and you need to fid it's vertex because that is the max height

h(t)= -16t² +96t +5

the x coordinate of the vertex is x= -b/2a for f(x)= ax²+bx+c so in our case

x=
`(-96)/(2*(-16))`= 3 , now we know that the vertex bbelongs to the graph so should verify the equation so we substitute t of the value of x=3 to find y

y= -16*3²+96*3+5= -144+288+5=149

the max height is the coordinate of y because it tels us how much it went up