Q. 78 - Precalculus Enhanced with Graphing Utilities

Question

Complete the square of the quadratic expression. Then graph the function using the technique of shifting.

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

Step-by-Step Solution

Answer

On completing the square of the quadratic expression, we get,

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

The required graph is given below,

Step 1. Given information.

Consider the given expression,

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

Add and subtract $2$ to the expression,

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

Step 2. Plot the graph.

Consider the given question,

First, draw the function $f\left(x\right)=x^2$.

Then shift it towards the left by $2$ to form $f\left(x\right)={\left(x+2\right)}^2$.

At last, shift it $2units$ downwards to get $f\left(x\right)={\left(x+2\right)}^2-2$.

Plot the graph,