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:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Count the x-intercepts

By looking at the graph, the horizontal axis represents time (\(x\)) and the vertical axis represents height (\(y\)). The parabola crosses the horizontal \(x\)-axis at exactly two distinct points.

Therefore, this parabola has 2 \(x\)-intercepts.

Step 2: Determine the height at the x-intercepts

The \(x\)-intercepts of any graph occur where the value of \(y\) is equal to \(0\). In this context, the vertical axis \(y\) represents the dolphin's height in feet.

Therefore, the \(x\)-intercepts represent the times when the dolphin's height above water is 0 feet.

Answer:

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