Q. 75 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The graph of the given equation is

Step 1. Given information

Given expression:

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

Step 2. Write the concept

In order to complete the square, we will add or subtract some numbers in order to simplify it

Step 3. Calculation

Let's add and subtract $1^2$ on right side therefore,

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

Step 4. Graphing using shifting technique

In order to graph the given expression we need to draw the graph of $y=x^2$ i.e.

Step 5. Graphing the actual expression

Replace $x+1$ by $x$ in the expression

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