Answer:
5 seconds
Step-by-step explanation:
Given the height function h(t) = -2x² + 2x + 40, you want the positive value of t such that h(t) = 0.
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.
