Question

Question 11:What is the maximum height of the driver off the diving board

Answer 1

`y=-(4)/(9)x^2+(24)/(9)x+12`

To find the maximun height (y) given a quadratic equation as above you find the coordinates of the vertex (maximum or minimun point of a parabola)

1. Use the next formula to find the x- coordinate of the vertex

`\begin{gathered} y=ax^2+bx+c \\ \\ x=-(b)/(2a) \end{gathered}`
`\begin{gathered} x=-((24)/(9))/(2(-(4)/(9))) \\ \\ x=-((24)/(9))/(-(8)/(9))=(-24)/(-8)=3 \end{gathered}`

2. Use the value of x above to find y-coordinate in the vertex:

`\begin{gathered} y=-(4)/(9)(3)^2+(24)/(9)(3)+12 \\ \\ y=-(4)/(9)(9)+(72)/(9)+12 \\ \\ y=-4+8+12 \\ \\ y=16 \end{gathered}`Then, the maximum height of the diver is 16 feet