Answer
$\begin{array}{ll}
a. & -4\\
b. & 1\\
c. & -3\\
d. & 3x^{2}-2x-4\\
e. & -3x^{2}-2x+4\\
f. & 3x^{2}+8x+1\\
g. & 12x^{2}+4x-4\\
h. & 3x^{2}+6xh+3h^{2}+2x+2h-4
\end{array}$
Work Step by Step
$f(x)=3x^{2}+2x-4$
$\begin{array}{lll}
(a)\ f(0) & (b)\ f(1) & (c)\ f(-1)\quad \\
=3(0)^{2}+2(0)-4 & =3(1)^{2}+2(1)-4 & =3(-1)^{2}+2(-1)-4\\
=-4 & =3+2-4 & =3-2-4\\
& =1 & =-3
\end{array}$
$\begin{array}{ll}
(d)\ f(-x) & (e)\ -f(x)\\
=3(-x)^{2}+2(-x)-4 & =-(3x^{2}+2x-4)\\
=3x^{2}-2x-4\quad & =-3x^{2}-2x+4\\
&
\end{array}$
$\begin{array}{lll}
(f)\ f(x+1) & (g)\ f(2x) & \\
=3(x+1)^{2}+2(x+1)-4 & =3(2x)^{2}+2(2x)-4 & \\
=3x^{2}+6x+3+2x+2-4 & =12x^{2}+4x-4 & \\
=3x^{2}+8x+1 & & \\
& &
\end{array}$
$(h)\ f(x+h)=3(x+h)^{2}+2(x+h)-4$
$=3(x^{2}+2xh+h^{2})+2x+2h-4$
$=3x^{2}+6xh+3h^{2}+2x+2h-4$
