Question

This parabola has
x-intercepts

Answer 1

This parabola has 2 x-intercepts

Representing the times when the dolphin's height above water is 0 feet

There are two real solutions to this equation, representing the number of seconds elapsed between the dolphin exiting and reentering the water.

Explanation:

That's all the answers for this whole slide :)

Answer 2

see the explanation

Explanation:

we have the quadratic equation

`y=-16x^(2) +32x-10`

This is a vertical parabola open downward

The vertex is a maximum

Find the x-intercepts of the quadratic equation

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

`-16x^(2) +32x-10=0`

Solve the quadratic equation

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`-16x^(2) +32x-10=0`

so

`a=-16\\b=32\\c=-10`

substitute in the formula

`x=\frac{-32(+/-)\sqrt{32^(2)-4(-16)(-10)}} {2(-16)}`

`x=\frac{-32(+/-)√(384)} {-32}`

`x=(-32(+/-)8√(6))/(-32)`

`x=(-32(+)8√(6))/(-32)=(32(-)8√(6))/(32)=0.39\ sec`

`x=(-32(-)8√(6))/(-32)=(32(+)8√(6))/(32)=1.61\ sec`

therefore

This parabola has two x-intercepts representing the times when the dolphin's height above water is zero feet