For the function f(x) = 4x^2 − 5x + 2, find and simplify each of the following. (a) f(y + 3) (b) f(1 + h) − f(1)

Answer 1

For each of these, just plug in the "thing" in parenthesis into the function wherever there is an "x". So for f(y+3) you would plug in "y + 3" in for x like this:

f(y+3) = 4(y + 3)² − 5(y + 3) + 2 and simplify:

f(y+3) = 4(y² + 6y + 9) − 5y − 15 + 2

f(y+3) = 4y² + 24y + 36 − 5y − 13

f(y+3) = 4y² + 19y + 23

Do the same for the other problem except first plug in "1 + h" and then plug in "1" and then subtract.

f(1 + h) = 4(1 + h)² − 5(1 + h) + 2

f(1 + h) = 4(1 + 2h + h² − 5 − 5h + 2

f(1 + h) = 4 + 8h + 4h² − 3 − 5h

f(1 + h) = 4h² + 3h + 1

Then do f(1) = 4(1)² − 5(1) + 2 = 4 - 5 + 2 = 1

The subtract to get:

f(1 + h) - f(1) = (4h² + 3h + 1) - (1)

f(1 + h) - f(1) = 4h² + 3h