Chapter 7.6, Problem 1WE

To determine

Sketch the graph of the function $f\left(x\right)=x^2-1$ .

Explanation of Solution

Given information: The given function is $f\left(x\right)=x^2-1$ .

Graph: The given function can be written as,

  $\begin{array}{c}y=x^2-\mathrm{1....}\left(\text{Replace }f\left(x\right)=y\right)\\ y+1=x^2\mathrm{....}\left(1\right)\end{array}$

Now (1) represents a parabola and its graph is shown as,

  

Observation: Since (1) represents a parabola of the form $y-k=a{\left(x-h\right)}^2$ . Therefore the graph for the function (1) has vertex $\left(0,-1\right)$ and axis of symmetry $x=0$ .