The height h in feet of a ball thrown into the air after t seconds is given by h(t) = 16t2 + 25t +3. Use synthetic substitution to find the high of the ball after 1.5 seconds.

Answer 1

Zalma I first need to point out a small typo in your equation. Due to the Earth's gravity the quadratic coefficient ("a") is ALWAYS -16 when measuring the height in feet. (Or -4.9 if using meters.) If you don't like these numbers, use a different unit to measure the height, or find yourself another planet to play ball on.

So, the coefficients for the corrected function are -16, 25 & 3.

To carry out the synthetic substitution using 1.5 for x follow these steps

1. Multiply the first coefficient by x, -16 x 1.5 = -24
2. Add that to the second coefficient, -24 + 25 = 1
3. Multiply that result by x, 1 x 1.5 = 1.5
4. Add that to the last coefficient, 1.5 + 3 = 4.5

The numeric part of the answer is 4.5 but remember a word problem gets a word answer.

A complete answer might read like this; "1.5 seconds after being thrown the height of the ball is 4.5 feet."

I hope this helps. I'm sure that with more practice you'll see the advantages of synthetic substitution.

Remember that it's important to practice, that's what makes the lesson "stick."