Question

1.) Alexander jumped off a cliff into the ocean in Acapulco while on vacation. His height as a function of time could be modeled by the function h(t) = -16t2 + 16t + 480, where t is the time in seconds and h is the height in feet. a. How long did it take for Alexander to reach his maximum height? b. What was the highest point that Alexander reached? c. Alexander hit the water after how many seconds? d. Make a sketch of graph of his dive.

Answer 1

so hmmm check the graph below

now.. to find the vertex of any quadratic


`\bf \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lccclll} h(t)=&-16t^2&+16t&+480\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)`

so... how long did it take? well, it took
`\bf -\cfrac{{{ b}}}{2{{ a}}}`

what was the highest point? well, it was
`\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}`

when did he hit the water? well, at y = 0
that is
`h(t) = -16t^2 + 16t + 480 \implies 0 = -16t^2 + 16t + 480,`

solve for "t"