Question Evaluate $y = x^{2} - 1$ for $x = -2, -1, 0, 1, 2$ . Plot the $(x, y)$ pairs and graph the function.

Studdy Solution

STEP 1

Assumptions
1. The formula to evaluate is $y = x^2 - 1$ .
2. The values of $x$ to be evaluated are -2, -1, 0, 1, and 2.

STEP 2

First, we will evaluate the formula for $x = -2$ .
$y = (-2)^2 - 1$

STEP 3

Calculate the square of -2.
$(-2)^2 = 4$

STEP 4

Substitute the value into the formula.
$y = 4 - 1$

STEP 5

Calculate the value of $y$ for $x = -2$ .
$y = 4 - 1 = 3$
Thus, when $x = -2$ , $y = 3$ .

STEP 6

Next, we will evaluate the formula for $x = -1$ .
$y = (-1)^2 - 1$

STEP 7

Calculate the square of -1.
$(-1)^2 = 1$

STEP 8

Substitute the value into the formula.
$y = 1 - 1$

STEP 9

Calculate the value of $y$ for $x = -1$ .
$y = 1 - 1 = 0$
Thus, when $x = -1$ , $y = 0$ .

STEP 10

Now, we will evaluate the formula for $x = 0$ .
$y = (0)^2 - 1$

STEP 11

Calculate the square of 0.
$(0)^2 = 0$

STEP 12

Substitute the value into the formula.
$y = 0 - 1$

STEP 13

Calculate the value of $y$ for $x = 0$ .
$y = 0 - 1 = -1$
Thus, when $x = 0$ , $y = -1$ .

STEP 14

Next, we will evaluate the formula for $x = 1$ .
$y = (1)^2 - 1$

STEP 15

Calculate the square of 1.
$(1)^2 = 1$

STEP 16

Substitute the value into the formula.
$y = 1 - 1$

STEP 17

Calculate the value of $y$ for $x = 1$ .
$y = 1 - 1 = 0$
Thus, when $x = 1$ , $y = 0$ .

STEP 18

Finally, we will evaluate the formula for $x = 2$ .
$y = (2)^2 - 1$

STEP 19

Calculate the square of 2.
$(2)^2 = 4$

STEP 20

Substitute the value into the formula.
$y = 4 - 1$

STEP 21

Calculate the value of $y$ for $x = 2$ .
$y = 4 - 1 = 3$
Thus, when $x = 2$ , $y = 3$ .

STEP 22

Now we will list the ordered pairs that we have found:
For $x = -2$ , $y = 3$ -> (-2, 3) For $x = -1$ , $y = 0$ -> (-1, 0) For $x = 0$ , $y = -1$ -> (0, -1) For $x = 1$ , $y = 0$ -> (1, 0) For $x = 2$ , $y = 3$ -> (2, 3)

STEP 23

To plot the graph of the function $y = x^2 - 1$ , we will plot the ordered pairs on a coordinate plane.

STEP 24

Draw a coordinate plane with an x-axis and a y-axis.

STEP 25

Plot the points (-2, 3), (-1, 0), (0, -1), (1, 0), and (2, 3) on the coordinate plane.

STEP 26

Connect the points with a smooth curve to represent the function $y = x^2 - 1$ , which is a parabola opening upwards.
The graph of the function has been plotted with the evaluated ordered pairs.

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