7.14.1 Evaluating Quadratic Functions in the Real World

Algebra 17.14.1 Evaluating Quadratic Functions in the Real World

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Warm Up

The height, in inches, of a frog's jump is modeled by the equation $h (t) = 60 t - 75 t^{2}$ , where the time $t$ , after the frog jumps, is measured in seconds.

1. For $h (t) = 60 t - 75 t^{2}$ :

a. Find $h (0)$ .

b. Find $h (0.8)$ .

2. What do these values of $h (0)$ and $h (0.8)$ mean in terms of the frog's jump?

Compare your answer:

They mean that the frog is on the ground when $t = 0$ (before jumping) and when $t = 0.8$ (when the frog lands on the ground).

3. After it jumped, how much time passed, in seconds, before the frog reached its maximum height?

0.4 seconds

4. Explain how you know this is the time the frog reached the maximum height.

Compare your answer:

The frog reached its maximum height at $t = 0.4$ , as that is the halfway point of the jump. If we graph the function, the vertex of the graph will have a horizontal coordinate ( $t$ -coordinate) of 0.4.

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
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