## The time a projectile spends in the air can be modeled by the equation t² -t – 8 = 0, in which t represents the amount of time traveled, in

Question

The time a projectile spends in the air can be modeled by the equation t² -t – 8 = 0, in which t represents the amount of time traveled, in seconds. Which of the following is equivalent to the equation t² – 2t – 8 = 0?
(t + 4)(t – 2) = 0
t -4)(t – 2) = 0
(t + 4)(t + 2) = 0
(t – 4) (t + 2) = 0

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3 months 2022-02-09T05:41:04+00:00 1 Answer 0 views 0

(t – 4)(t + 2) = 0

Step-by-step explanation:

The general formula for a quadratic expression is

y = ax² + bx + c

y = t² – 2t – 8 = 0

By comparison, we see that

a = 1; b = -2; c = -8

1. Find two numbers that multiply to give ac and add to give b.

In this case, find two numbers that multiply to give -8 and add to give -2.

It helps to list the factors of  -8.

They are ±1, ±2, ±4, and ±8

After a little trial and error, you should find the numbers -4 and +2.

-4 × 2 = -8, and -4 + 2 = -2)

2. Rewrite the middle term with those numbers

t² -4t + 2t – 8 = 0

3. Factor the first and last pairs of terms separately

t(t – 4) +2(t – 4) = 0

4. Separate the common factor

The common factor is t – 4.

(t – 4)(t + 2) = 0