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Chapter 7: Problem 21

Graph each equation in Exercises 21-32. Select integers for \(x\) from \(-3\) to 3 , inclusive. \(y=x^{2}-2\)

Short Answer

Expert verified
The plot of the quadratic equation \(y=x^{2}-2\) reveals a parabolic curve opening upwards. Points on the graph include (-3,7), (-2,2), (-1,-1), (0,-2), (1,-1), (2,2), (3,7).

Step by step solution

01

Select Values for \(x\)

Select all integer values for \(x\) from \(-3\) to 3, inclusive. These are \(-3, -2, -1, 0, 1, 2, 3\).
02

Substitute \(x\) and Calculate \(y\)

Substitute each selected \(x\) value into the equation \(y=x^{2}-2\) to find corresponding \(y\) values. This yields: \(x=-3, y=(-3)^2-2=7;\) \(x=-2, y=(-2)^2-2=2;\) \(x=-1, y=(-1)^2-2=-1;\) \(x=0, y=(0)^2-2=-2;\) \(x=1, y=(1)^2-2=-1;\) \(x=2, y=(2)^2-2=2;\) \(x=3, y=(3)^2-2=7.\)
03

Plot the Points

On a coordinate plane, plot the points identified in Step 2: (-3,7), (-2,2), (-1,-1), (0,-2), (1,-1), (2,2), (3,7).
04

Draw the Graph

Connect the points on the graph with a smooth curve to complete the graph of the quadratic function \(y=x^{2}-2\).

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