Question

graph the equation.

\\y = x^2 - 5\\

first plot the solutions of the equation for the given values of \\(x\\), and then connect the points with a smooth curve. (click the submit button to grade your response.)

\\x = -3, -2, -1, 0, 1, 2, 3\\

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline -3 & \\\\ \\hline -2 & \\\\ \\hline -1 & \\\\ \\hline 0 & \\\\ \\hline 1 & \\\\ \\hline 2 & \\\\ \\hline 3 & \\\\ \\hline \\end{array}$$

Explanation:

Evaluate negative inputs

Using the Function Evaluation and Quadratic Functions knowledge points, we substitute \(x = -3, -2, -1\) into the equation \(y = x^2 - 5\):

• For \(x = -3\):

$$y = (-3)^2 - 5 = 9 - 5 = 4$$

• For \(x = -2\):

$$y = (-2)^2 - 5 = 4 - 5 = -1$$

• For \(x = -1\):

$$y = (-1)^2 - 5 = 1 - 5 = -4$$

Evaluate zero input

Using the Function Evaluation and Quadratic Functions knowledge points, we substitute \(x = 0\) into the equation \(y = x^2 - 5\):

• For \(x = 0\):

$$y = (0)^2 - 5 = 0 - 5 = -5$$

Evaluate positive inputs

Using the Function Evaluation and Quadratic Functions knowledge points, we substitute \(x = 1, 2, 3\) into the equation \(y = x^2 - 5\):

• For \(x = 1\):

$$y = (1)^2 - 5 = 1 - 5 = -4$$

• For \(x = 2\):

$$y = (2)^2 - 5 = 4 - 5 = -1$$

• For \(x = 3\):

$$y = (3)^2 - 5 = 9 - 5 = 4$$

Answer:

\(x\)	\(y\)
\(-2\)	\(-1\)
\(-1\)	\(-4\)
\(0\)	\(-5\)
\(1\)	\(-4\)
\(2\)	\(-1\)
\(3\)	\(4\)