This question that I'm having problems with.

Question

The path of a diver is given by y = - 4/7x^2 + 8/7x+ 7

where y is the height in feet and x is the horizontal distance from the end of the diving board in feet. What is the maximum height of the diver? (Round your answer to one decimal place.)

Answer 1

You know this graph is a parabola because it's a quadratic equation. You know this parabola is upside down because of the sign in front of the first term. So if you find the vertex, you will find the max y-value. The max y-value is the maximum height of the diver.

First find the x-value at the vertex using the formula x = -b/2a. This will give you x = (-8/7)/(2*-4/7)=1.

Now find the y-value at the vertex by plugging in the x-value at the vertex into the quadratic formula. y=(-4/7)(1^2)+(8/7)(1)+7=7.6 when rounded to one decimal place.

The maximum height of the diver is 7.6 ft.

You may find it helpful to graph the quadratic formula and to see the curve. Try it out and see!