Problem
Consider the equation $y=x^{2}+1$. a) Using the given inputs, complete the table by entering the corresponding ordere pairs separated by commas. $\begin{array}{llllll}x & -2 & -1 & 0 & 1 & 2\end{array}$ $y$ b) Graph the equation by plotting the vertex and one other point. CHECK ANSWER
Solution
Step 1 ：Given the equation \(y=x^{2}+1\).
Step 2 ：Substitute the given x values into the equation to find the corresponding y values.
Step 3 ：For \(x=-2\), \(y=(-2)^{2}+1=5\). So, the ordered pair is (-2,5).
Step 4 ：For \(x=-1\), \(y=(-1)^{2}+1=2\). So, the ordered pair is (-1,2).
Step 5 ：For \(x=0\), \(y=(0)^{2}+1=1\). So, the ordered pair is (0,1).
Step 6 ：For \(x=1\), \(y=(1)^{2}+1=2\). So, the ordered pair is (1,2).
Step 7 ：For \(x=2\), \(y=(2)^{2}+1=5\). So, the ordered pair is (2,5).
Step 8 ：\(\boxed{\text{The corresponding ordered pairs are (-2,5), (-1,2), (0,1), (1,2), and (2,5).}}\)
