Question

I HAVE ONE WEEK OF SCHOOL CAN SOMEONE HELP?!

Answer 1

9514 1404 393

Answer:

  1. 5 seconds

  2. 4.5 seconds

Step-by-step 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."