Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The required graph is 

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 $h \mathrm{and} k$.

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

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.