Question

Find seven ordered pairs to the equation y=x^2-1. Then determine its graph.
x = -3 y= blank

Answer 1

To find ordered pairs for the equation \( y = x^2 - 1 \), we can substitute various values for \( x \) and calculate the corresponding \( y \) values.

Let's calculate \( y \) for \( x = -3 \):

\[
y = (-3)^2 - 1 = 9 - 1 = 8
\]

So the first ordered pair is \((-3, 8)\).

Now, let’s find six more ordered pairs by substituting different values for \( x \):

1. **For \( x = -2 \)**:
\[
y = (-2)^2 - 1 = 4 - 1 = 3 \quad \Rightarrow \quad (-2, 3)
\]

2. **For \( x = -1 \)**:
\[
y = (-1)^2 - 1 = 1 - 1 = 0 \quad \Rightarrow \quad (-1, 0)
\]

3. **For \( x = 0 \)**:
\[
y = (0)^2 - 1 = 0 - 1 = -1 \quad \Rightarrow \quad (0, -1)
\]

4. **For \( x = 1 \)**:
\[
y = (1)^2 - 1 = 1 - 1 = 0 \quad \Rightarrow \quad (1, 0)
\]

5. **For \( x = 2 \)**:
\[
y = (2)^2 - 1 = 4 - 1 = 3 \quad \Rightarrow \quad (2, 3)
\]

6. **For \( x = 3 \)**:
\[
y = (3)^2 - 1 = 9 - 1 = 8 \quad \Rightarrow \quad (3, 8)
\]

Now we have the following seven ordered pairs:

1. \((-3, 8)\)
2. \((-2, 3)\)
3. \((-1, 0)\)
4. \((0, -1)\)
5. \((1, 0)\)
6. \((2, 3)\)
7. \((3, 8)\)

### Graphing the Equation

The equation \( y = x^2 - 1 \) represents a parabola that opens upwards. The vertex of the parabola is at the point \((0, -1)\).

Here’s a rough idea of how you would plot the points:

1. Start by marking the vertex \((0, -1)\).
2. Plot each of the ordered pairs you calculated.
3. Since this is a quadratic function, the graph will be symmetrical about the y-axis.

The graph will look like this:

\[
\text{Graph of } y = x^2 - 1
\]

To visualize it, you would draw a smooth curve through the points you plotted, creating a U-shaped parabola.