Question

A diver dives from the board at a local swimming pool. Her height, y, in metres, above the water in terms of her horizontal distance, x, in metres, from the end of the board is given by y= -x^2 + 2x + 3. What is the diver's maximum height?

Answer 1

4 meters

Explanation:

Given a quadratic equation in which the coefficient of
`x^2` is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.

Since the divers height, y is modeled by the equation

`y= -x^2 + 2x + 3`

Step 1: Determine the equation of symmetry

In the equation above, a=-1, b=2, c=3

Equation of symmetry,
`x=-(b)/(2a)`

`x=-(2)/(2*-1)\\x=1`

Step 2: Find the value of y at the point of symmetry

That is, we substitute x obtained above into the y and solve.

`y(1)= -1^2 + 2(1) + 3=-1+2+3=4m`

The maximum height of the diver is therefore 4 meters.