Section 3.1 : Graphing
5. Determine the \(x\)-intercepts and the \(y\)-intercepts for the following equation.
\[y = 6 - {x^2}\]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,
\[\begin{align*}y & = 6 - {\left( 0 \right)^2}\\ y & = 6\end{align*}\]The \(y\)-intercept for this equation is then the point : \(\left( {0,6} \right)\) .
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,
\[\begin{align*}0 & = 6 - {x^2}\\ {x^2} & = 6\\ x & = \pm \sqrt 6 \end{align*}\]The \(x\)-intercepts for this equation are then the two points : \(\left( { - \sqrt 6 ,0} \right)\) and \(\left( {\sqrt 6 ,0} \right)\) .