Question

dolphins jump out of the water, or breach, for a number of reasons, including communication, display, and feeding. a scientist is tracking the movement of a dolphin as it breaches. the dolphin’s distance above or below the surface of the water, in feet, after t seconds can be modeled by the expression -16(t - 1.5)² + 19. complete the sentence. the dolphin jumped out of the water and reached a maximum height of feet above the water’s surface. submit

Explanation:

Step1: Identify the vertex form

The given expression is in vertex form of a quadratic function \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, the expression is \( -16(t - 1.5)^2 + 19 \), so \( a=-16 \), \( h = 1.5 \), and \( k = 19 \).

Step2: Analyze the vertex for maximum/minimum

Since \( a=-16<0 \), the parabola opens downward, so the vertex represents the maximum point. The \( k \)-value of the vertex gives the maximum height.

Answer:

19