Question

For the function $f\left(x\right)=2x^2+4x-3$, evaluate the function.

1. $f\left(2\right)$
   
2. $f\left(-3\right)$
   
3. $f\left(h\right)$
   

Short answer

Part (a) $f\left(2\right)=13$

Part (b)$f\left(-3\right)=3$

Part (c) $f\left(h\right)=2h^2+4h-3$

Step-by-step solution

Part (a) Step 1.

Substitute $x=2$in $f\left(x\right)=2x^2+4x-3$,

$\begin{array}{rcl}f\left(2\right)& =& 2{\left(2\right)}^2+4\left(2\right)-3\\ & =& 2\left(4\right)+8-3\\ & =& 8+5\\ & =& 13\end{array}$

Part (b) Step 1.

Substitute $x=-3$in localid="1644633261905" $f\left(x\right)=2x^2+4x-3$,

$$\begin{gathered} f(-3)=2{(-3)}^2+4(-3)-3 \\ f(-3)=18-12-3 \\ f(-3)=3 \end{gathered}$$

Part (c) Step 1.

Substitute $x=h$inlocalid="1644633275522" $f\left(x\right)=2x^2+4x-3$,

localid="1644633469575" $\begin{array}{rcl}f\left(h\right)& =& 2{\left(h\right)}^2+4\left(h\right)-3\\ & =& 2h^2+4h-3\end{array}$