Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 3.1 : Graphing
8. Determine the \(x\)-intercepts and the \(y\)-intercepts for the following equation.
\[y = {x^2} + 6x + 58\]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,
\[\begin{align*}y & = {\left( 0 \right)^2} + 6\left( 0 \right) + 58\\ y & = 58\end{align*}\]The \(y\)-intercept for this equation is then the point : \(\left( {0,58} \right)\) .
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,
\[\begin{align*}0 & = {x^2} + 6x + 58\\ x & = \frac{{ - 6 \pm \sqrt {{6^2} - 4\left( 1 \right)\left( {58} \right)} }}{{2\left( 1 \right)}} = \frac{{ - 6 \pm \sqrt { - 196} }}{2} = \frac{{ - 6 \pm 14\,i}}{2} = - 3 \pm 7i\end{align*}\]Because we got complex solutions to this equation we know that this equation has no x‑intercepts.