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Section 3.1 : Graphing
7. Determine the \(x\)-intercepts and the \(y\)-intercepts for the following equation.
\[y = {x^2} + 10\]Show All Steps Hide All Steps
Start SolutionRecall that in order to find the \(y\)-intercept all we need to do is plug \(x = 0\) into the equation and solve for \(y\). Doing that for this equation gives,
\[\begin{align*}y & = {\left( 0 \right)^2} + 10\\ y & = 10\end{align*}\]The \(y\)-intercept for this equation is then the point : \(\left( {0,10} \right)\) .
Show Step 2Finding the \(x\)-intercept is similar to the \(y\)-intercept. All we do is plug in \(y = 0\) and solve for \(x\). Doing that for this equation gives,
\[\begin{align*}0 & = {x^2} + 10\\ {x^2} & = - 10\\ x & = \pm \sqrt { - 10} = \pm \sqrt {10} \,i\end{align*}\]Because we got complex solutions to this equation we know that this equation has no x‑intercepts.