Question

An astronaut on the moon throws a baseball upward. The height of the ball in feet

(y) is related to the number of seconds since the ball was thrown (x).
y = -2.7x² + 30x + 6.5
How high will the ball be after 3 seconds? Use your calculator to pull up a function
table to help you. (6 points total)
a.
b.
Height after 3 seconds =
feet. (2 points)
Give two approximate times (in seconds) that the ball will be at a height of
75 feet.
and
seconds (on its way up). (2 points)
seconds (on its way down). (2 points)

Answer 1

y = feet in the air

x = seconds it takes

well, what's "y" when x = 3?

`y=-2.7(3)^2 + 30(3) + 6.5\implies y=-2.7(9)+96.5\implies \boxed{y=72.2~feet}`

now, what's "x" when y = 75?

`75=-2.7x^2+30x+6.5\implies 0=-2.7x^2+30x-68.5 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-2.7}x^2\stackrel{\stackrel{b}{\downarrow }}{+30}x\stackrel{\stackrel{c}{\downarrow }}{-68.5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}`

`x=\cfrac{-30\pm√((30)^2 - 4(-2.7)(-68.5))}{2(-2.7)}\implies x=\cfrac{-30\pm√(900-739.8)}{-5.4} \\\\\\ x=\cfrac{30\mp√(160.2)}{5.4}\implies x\approx \begin{cases} 3.2&\textit{on the way up}\\\\ 7.9&\textit{on the way down} \end{cases}`