Question

A ball is shot into the air using a brand new super-high-tech robotic arm to help baseball players practice catch fly balls.

Answer 1

Answer:

69 feet

Step-by-step explanation:

we have

$h(t)=-16t^{2}+64t+5$

where

h(t) is the height of the ball

t is the time in seconds

we know that the given equation is a vertical parabola open downward

The vertex is the maximum

so

the y-coordinate of the vertex represent the maximum height of the ball

Convert the quadratic equation into vertex form

The equation in vertex form is equal to

$y=(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

$h(t)=-16t^{2}+64t+5$

$h(t)-5=-16t^{2}+64t$

$h(t)-5=-16(t^{2}-4t)$

$h(t)-5-64=-16(t^{2}-4t+4)$

$h(t)-69=-16(t^{2}-4t+4)$

$h(t)-69=-16(t-2)^{2}$

$h(t)=-16(t-2)^{2}+69$

the vertex is the point (2,69)

therefore

The maximum height is 69 ft