Question

A swimmer dives into the pool from a 6 foot platform modeled by the following y=x- 12x + 6. What was the maximum depth that the swimmer reached?

Answer 1

The expression that models the swimmer dive is given by:

`y=x^2-12x+6`

Which is a parabolla, the maximum depth of the swimmer will be the value of "y" that corresponds to the vertex of this shape. We can calculate the vertex of the parabola by using the following formula:

`x=-(b)/(2a)`

Whera a is the number multiplying x² and b is the number multiplying x. Applying the data from the problem we have:

`x=-((-12))/(2)=6`

We can now find the depth by applying this value of x to the expression, we have:

`\begin{gathered} y=(6)^2-12\cdot6+6 \\ y=36-72+6 \\ y=30 \end{gathered}`

The maximum depth was 30 feet.