Chapter 3, Problem 3CLT

To determine

To sketch: the equation $y=x^2-9$ .

Explanation of Solution

Given:

The equation is $y=x^2-9$ .

Calculation:

Steps of making sketch are:

• Take the some of values of x as 1, 2, 0 etc.
• Find the corresponding values of y.
• Draw the coordinates on the plot and join them.

For x = 0,

  $\begin{array}{l}y={\left(0\right)}^2-9\\ y=-9\end{array}$

For x = 1,

  $\begin{array}{l}y={\left(1\right)}^2-9\\ y=-8\end{array}$

For x = -1,

  $\begin{array}{l}y={\left(-1\right)}^2-9\\ y=-8\end{array}$

For x = 3,

  $\begin{array}{c}y={\left(3\right)}^2-9\\ =0\end{array}$

For x = -3,

  $\begin{array}{c}y={\left(-3\right)}^2-9\\ =0\end{array}$

Thus, the coordinates are $\left(0,-9\right)$ , $\left(1,-8\right)$ , $\left(-1,-8\right)$ , $\left(-3,0\right)$ and $\left(3,0\right)$ .

The required plot is shown below: