Question

A plastic boulder was launched from a second-floor window, using a catapult. The function below represents the height of the

plastic boulder from the ground, h(t), in feet, over time, t, in seconds.
h(t) = -2x² + 2x + 40
How many seconds did it take for the plastic boulder to hit the ground?

Answer 1

5 seconds

Explanation:

Given the height function h(t) = -2x² + 2x + 40, you want the positive value of t such that h(t) = 0.

Solution

The given function can be factored as ...

h(t) = -2(x -5)(x +4)

This will be zero when the factors are zero:

x -5 = 0 ⇒ x = 5

x +4 = 0 ⇒ x = -4

The positive value of t for which the height is zero is t = 5.

It took 5 seconds for the plastic boulder to hit the ground.

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Additional comment

There are several methods available for factoring the equation. One is to factor out the leading coefficient, then factor the remaining quadratic.

-2(x² -x -20)

To factor this, you're looking for factor pairs of -20 that have a sum of -1.

-20 = -20(1) = -10(2) = -5(4)

The last of these, {-5, 4} has a sum of -1. These are the constants that go into the binomial factors.