Find and simplify f (x + h).
-$$f ( x ) = - 3 x ^ { 2 } + 2 x + 1$$
A) $- 3 x ^ { 2 } 2 x h + h ^ { 2 } + 2 x + 2 h + 1$
B) $- 3 x ^ { 2 } - 3 h ^ { 2 } + 2 x + 2 h + 1$
C) $- 3 x ^ { 2 } - 6 x h - 3 h ^ { 2 } + 2 x + 2 h + 1$
D) $- 3 x ^ { 2 } - 3 h ^ { 2 } + 2 x h + 1$

Question

Quizplus · Accepted Answer

To find $f(x + h)$, substitute $x + h$ for $x$ in the given function $f(x) = -3x^2 + 2x + 1$. This results in $f(x + h) = -3(x + h)^2 + 2(x + h) + 1$. Expanding $(x + h)^2$ gives $x^2 + 2xh + h^2$, and substituting this back into the equation yields $-3(x^2 + 2xh + h^2) + 2x + 2h + 1$, which simplifies to $-3x^2 - 6xh - 3h^2 + 2x + 2h + 1$.

Find and Simplify F (X + H) f(x)=−3x2+2x+1f ( x ) = - 3 x ^ { 2 } + 2 x + 1f(x)=−3x2+2x+1

Find and Simplify F (X + H) $f ( x ) = - 3 x ^ { 2 } + 2 x + 1$