Question

find and simplify $f(x + h)$. simplify your answer. $f(x) = -8x^2 - 2x + 3$ $f(x + h) = \square$

Explanation:

Step1: Substitute $x+h$ into $f(x)$

$f(x+h) = -8(x+h)^2 - 2(x+h) + 3$

Step2: Expand $(x+h)^2$ and distribute terms

$f(x+h) = -8(x^2+2xh+h^2) -2x -2h + 3$

Step3: Distribute the -8 to the polynomial

$f(x+h) = -8x^2 -16xh -8h^2 -2x -2h + 3$

Step4: Combine like terms (no like terms left to combine)

$f(x+h) = -8x^2 -16xh -8h^2 -2x -2h + 3$

Answer:

$-8x^2 -16xh -8h^2 -2x -2h + 3$