91Ó°ÊÓ

We have:

$f\left(x\right)=2x^2+4x+6$

The function is $f\left(x\right)=2x^2+4x+6$.

Add the some value to both sides:

$f\left(x\right)=2\left(x^2+2x\right)+6$

Add $2×1$to the both sides:

$$\begin{gathered} f\left(x\right)+2=2\left(x^2+2x+1\right)+6 \\ f\left(x\right)+2=2{(x+1)}^2+6f\left(x\right)=2{(x+1)}^2+6-2 \\ f\left(x\right)=2{(x+1)}^2+4 \end{gathered}$$

The parent function of the function is $f\left(x\right)=x^2$.

At $x=0:$

$$\begin{gathered} f\left(0\right)=0^2 \\ =0 \end{gathered}$$

By the same procedure find some points:

localid="1645545268940" $\left(-3,9\right),\left(-2,4\right),\left(0,0\right),\left(2,4\right),\left(3,9\right)$

Plot the calculated points. Draw a smooth curve through the plotted points. The graph of $f\left(x\right)=x^2$ is shown below. The graph of $f\left(x\right)=x^2$is horizontally translate to the left by $1$unit. The transform equation will be $f\left(x\right)={\left(x+1\right)}^2$. The graph of $f\left(x\right)={\left(x+1\right)}^2$is horizontally shrinks by a factor $2.$The transform equation will be $f\left(x\right)=2{\left(x+1\right)}^2$. The graph of $f\left(x\right)=2{\left(x+1\right)}^2$is vertically translated upward by $4$units. The transform equation will by $f\left(x\right)=2{\left(x+1\right)}^2+4$.