Q. 77 - Precalculus Enhanced with Graphing Utilities

Question

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

$f\left(x\right)=x^2-8x+1$

Step-by-Step Solution

Answer

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

$f\left(x\right)={\left(x-4\right)}^2-15$

The required graph is given below,

Step 1. Given information.

Consider the given expression,

$f\left(x\right)=x^2-8x+1$

Add and subtract $16$ to the expression,

$$\begin{gathered} f\left(x\right)=x^2-8x+16+1-16 \\ f\left(x\right)={\left(x-4\right)}^2-15 \end{gathered}$$

Step 2. Plot the graph.

Consider the given question,

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

Then shift it towards the right by $4units$ to form $f\left(x\right)={\left(x-4\right)}^2$.

At last, shift it $15units$ downwards to get $f\left(x\right)={\left(x-4\right)}^2-15$.

Plot the graph,