Question

Find and simplify each of the following for f(x) = 4x² - 6x + 9.

(A) f(x + h) =
(Do not factor.)

Answer 1

ANSWER -

To find f(x+h), we need to substitute (x+h) for x in the equation f(x) = 4x² - 6x + 9.

f(x+h) = 4(x+h)² - 6(x+h) + 9

= 4x² + 8xh + 4h² - 6x - 6h + 9

= 4x² - 6x + 9 + 8xh + 4h² - 6h

= f(x) + 8xh + 4h² - 6h

So, f(x+h) = 4x² - 6x + 9 + 8xh + 4h² - 6h.