9514 1404 393
Answer:
1. 5 seconds
2. 4.5 seconds
Explanation:
Both of these questions can be solved the same way. Each quadratic gives height as a function of time. You're interested in the time at which the height is zero. Factor the quadratic and find the positive value of x that makes the relevant factor be zero.
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1) y = -15x(x -5)
x = 5 makes the second factor zero
The golf ball is in the air 5 seconds.
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2) y = -12x(x -4.5)
x = 4.5 makes the second factor zero
The football is in the air for 4.5 seconds.
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Additional comment
The "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. When a factored quadratic (or any other polynomial) is zero, one of the factors must be zero. If the factor is of the form (ax+b), then the corresponding solution is ...
ax+b = 0 ⇒ ax = -b ⇒ x = -b/a
That is, once you have the factored form, you can write the solutions "by inspection."