Question

dolphin jump

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

this parabola has x-intercepts,

representing the times when the dolphins height above water is feet.

Explanation:

Step1: Find the number of x-intercepts

Calculate the discriminant \(D = b^2 - 4ac\) for \(y = -16x^2 + 32x - 10\).

$$D = 32^2 - 4(-16)(-10) = 1024 - 640 = 384$$

Since \(D > 0\), there are 2 x-intercepts.

Step2: Determine the height at x-intercepts

Identify the physical meaning of the x-intercepts where \(y = 0\).

$$y = 0$$

Answer:

This parabola has 2 x-intercepts, representing the times when the dolphin's height above water is 0 feet.