Question

How do you graph $$y=x^2-4$$ ?

Answer 1

Hint: Here we have to plot a graph. In this given equation by giving the values to the x like 0, 1, 2, 3, … simultaneously we get the values of y with respect to the x value. After getting the x and y values, write the coordinates of the given equation in the form of (x,y), by using the coordinates construct the required graph of the given equation.

Complete step-by-step answer:
Given equation in the form of linear equation in the form of two variables x and y
Consider the equation $$y=x^2-4$$
Now, by giving the x values … -3, -2, -1, 0, 1, 2, 3, … to the above equation simultaneously we get the values of y
When we substitute the value of x=-3, then
 $$\Rightarrow y={\left(-3\right)}^2-4$$
 $$\Rightarrow y=9-4$$
 $$\therefore y=5$$
Therefore, co-ordinate $$\left(x,y\right)=\left(-3,5\right)$$
When we substitute the value of x=-2
 $$\Rightarrow y={\left(-2\right)}^2-4$$
 $$\Rightarrow y=4-4$$
 $$\therefore y=0$$
Therefore, co-ordinate $$\left(x,y\right)=\left(-2,0\right)$$
When we substitute the value of x=-1
 $$\Rightarrow y={\left(-1\right)}^2-4$$
 $$\Rightarrow y=1-4$$
 $$\therefore y=-3$$
 Therefore, co-ordinate $$\left(x,y\right)=\left(-1,-3\right)$$
When we substitute the value of x=0
 $$\Rightarrow y={\left(0\right)}^2-4$$
 $$\Rightarrow y=0-4$$
 $$\therefore y=-4$$
 Therefore, co-ordinate $$\left(x,y\right)=\left(0,-4\right)$$
When we substitute the value of x=1
 $$\Rightarrow y={\left(1\right)}^2-4$$
 $$\Rightarrow y=1-4$$
 $$\therefore y=-3$$
 Therefore, co-ordinate $$\left(x,y\right)=\left(1,-3\right)$$
When we substitute the value of x=2
 $$\Rightarrow y={\left(2\right)}^2-4$$
 $$\Rightarrow y=4-4$$
 $$\therefore y=0$$
Therefore, co-ordinate $$\left(x,y\right)=\left(2,0\right)$$
When we substitute the value of x=3, then
 $$\Rightarrow y={\left(3\right)}^2-4$$
 $$\Rightarrow y=9-4$$
 $$\therefore y=5$$
Therefore, co-ordinate $$\left(x,y\right)=\left(3,5\right)$$
And so on …
Hence by substituting the value of x we have determined some of the values or points we use to plot the graph.
The coordinates can be written in table as :

$$x$$	$$-3$$	$$-2$$	$$-1$$	$$0$$	$$1$$	$$2$$	$$3$$
$$y$$	$$5$$	$$0$$	$$-3$$	$$-4$$	$$-3$$	$$0$$	$$5$$
$$\left(x,y\right)$$	$$\left(-3,5\right)$$	$$\left(-2,0\right)$$	$$\left(-1,-3\right)$$	$$\left(0,-4\right)$$	$$\left(1,-3\right)$$	$$\left(2,0\right)$$	$$\left(3,5\right)$$

Hence, the graph of the given linear equation $$y=x^2-4$$ represent the parabola is given by

Note: The question belongs to the concept of graph. By comparing the given equation to the equation of a line we calculate the slope and intercept. Or by choosing the value of x we can determine the value of y and then plotting the graphs for these points we obtain the result.