Question

In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).

$f\left(x\right)=2{\left(x+1\right)}^2+4$

Short answer

The required graph is

Step-by-step solution

Step 1. Given information.

The given quadratic function is$f\left(x\right)=2{\left(x+1\right)}^2+4$.

Step 2. Determine the horizontal and vertical shift.

Compare the function with $f\left(x\right)={\left(x-h\right)}^2+k$and determine $h\mathrm{and}k$.

role="math" localid="1646225202234" $$\begin{gathered} f\left(x\right)=2{\left(x+1\right)}^2+4 \\ f\left(x\right)=a{\left(x-h\right)}^2+k \\ So,h=-1 \\ k=4 \\ a=2 \end{gathered}$$

Plot the graph  of the parent function. 

Plot the graph of $f\left(x\right)=x^2$.

Step 4. Stretch the graph.

Stretch the graph of $f\left(x\right)=x^2$vertically 2 unit.

Step 5. Horizontal and vertically shift the graph.

Shift the graph of $f\left(x\right)=2x^2$vertically and horizontally, left 1 unit and and up 4 units.