Questions: For the equation y=x^2-7, (a) create a table with at least three ordered pairs that are solutions of the equation, and (b) graph the equation. (a) Complete the following table of ordered pairs that are solutions of the equation. x y -2 -3 0 -7 2 -3 (b) Use the graphing tool to graph the equation.

Solution Steps

The given equation is \( y = x^2 - 7 \). We need to create a table with at least three ordered pairs that are solutions of the equation and then graph the equation.

Select three values for \( x \). Common choices are \( x = -2 \), \( x = 0 \), and \( x = 2 \).

Substitute the chosen \( x \) values into the equation to find the corresponding \( y \) values.

• For \( x = -2 \): \( y = (-2)^2 - 7 = 4 - 7 = -3 \)
• For \( x = 0 \): \( y = 0^2 - 7 = -7 \)
• For \( x = 2 \): \( y = 2^2 - 7 = 4 - 7 = -3 \)

The ordered pairs are:

• \( (-2, -3) \)
• \( (0, -7) \)
• \( (2, -3) \)

Plot the points \( (-2, -3) \), \( (0, -7) \), and \( (2, -3) \) on the graph.

Connect the points with a smooth curve to represent the graph of the equation \( y = x^2 - 7 \).

Final Answer