Question

A swim team member performs a dive from a 14-foot high springboard. The parabola below shows the path of her dive. Create the equation that represents the path of the diver. 24 20 16 Height (feet) 12 8 4 0 2 6 10 Distance from Springboard (feet) Q + Page 5 1 6 domi ch

Answer 1

The equation of a parabola in vertex form is:

`f(x)=a(x-h)^2+k`

Where (h,k) are the coordinates of the vertex of the parabola.

From the picture, notice that the vertex of the parabola has coordinates (3,23), then:

`\begin{gathered} h=3 \\ k=23 \end{gathered}`

Then, our function reduces to:

`f(x)=a(x-3)^2+23`

Evaluate the function at x=0 to find the value of a. Notice from the figure that f(0)=14. On the other hand:

`\begin{gathered} f(0)=a(0-3)^2+23 \\ \Rightarrow f(0)=a\cdot9+23 \\ \Rightarrow f(0)=9a+23 \end{gathered}`

Since f(0)=14 then:

`\begin{gathered} 14=9a+23 \\ \Rightarrow9a=14-23 \\ \Rightarrow9a=-9 \\ \Rightarrow a=-(9)/(9) \\ \therefore a=-1 \end{gathered}`

Therefore, the function that describes this situation is:

`f(x)=-(x-3)^2+23`