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.

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.
Transcript text: 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. \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-2 & -3 \\ \hline 0 & -7 \\ \hline 2 & -3 \\ \hline \end{tabular} (b) Use the graphing tool to graph the equation.
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Solution

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Solution Steps

Step 1: Identify the equation and the task

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.

Step 2: Choose values for \( x \)

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

Step 3: Calculate corresponding \( y \) values

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 \( x = 2 \): \( y = 2^2 - 7 = 4 - 7 = -3 \)
Step 4: Create the table of ordered pairs

The ordered pairs are:

  • \( (-2, -3) \)
  • \( (0, -7) \)
  • \( (2, -3) \)
Step 5: Plot the points on the graph

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

Step 6: Draw the graph of the equation

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

Final Answer

The table of ordered pairs is: \[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & -3 \\ 0 & -7 \\ 2 & -3 \\ \hline \end{array} \] The graph of the equation \( y = x^2 - 7 \) is a parabola opening upwards with its vertex at \( (0, -7) \).

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