Questions: Show that (-3,-8) is not a point on the graph of y=x^2+1, and show that (-3,10) is on the graph of the function. (Do not refer to a graph of the equation. Use the formula to determine what point is or is not a solution to the equation.)

Show that \((-3, -8)\) is not a point on the graph of \(y = x^{2} + 1\).

Substitute \(x = -3\) into the equation.

Substitute \(x = -3\) into \(y = x^{2} + 1\):
\[ y = (-3)^{2} + 1 = 9 + 1 = 10. \]

Compare the calculated \(y\)-value with the given point.

The calculated \(y\)-value is \(10\), but the given point has \(y = -8\). Since \(10 \neq -8\), the point \((-3, -8)\) is not on the graph of \(y = x^{2} + 1\).

\(\boxed{(-3, -8) \text{ is not on the graph of } y = x^{2} + 1.}\)

Show that \((-3, 10)\) is on the graph of \(y = x^{2} + 1\).

Substitute \(x = -3\) into the equation.

Substitute \(x = -3\) into \(y = x^{2} + 1\):
\[ y = (-3)^{2} + 1 = 9 + 1 = 10. \]

Compare the calculated \(y\)-value with the given point.

The calculated \(y\)-value is \(10\), which matches the \(y\)-coordinate of the given point \((-3, 10)\). Therefore, \((-3, 10)\) is on the graph of \(y = x^{2} + 1\).

\(\boxed{(-3, 10) \text{ is on the graph of } y = x^{2} + 1.}\)

\(\boxed{(-3, -8) \text{ is not on the graph of } y = x^{2} + 1.}\)
\(\boxed{(-3, 10) \text{ is on the graph of } y = x^{2} + 1.}\)