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Section 3.1 : Graphing
6. Determine the \(x\)-intercepts and the \(y\)-intercepts for the following equation.
\[y = {x^2} + 6x - 7\]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,
\[\begin{align*}y & = {\left( 0 \right)^2} + 6\left( 0 \right) - 7\\ y & = - 7\end{align*}\]The \(y\)-intercept for this equation is then the point : \(\left( {0, - 7} \right)\) .
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,
\[\begin{align*}0 & = {x^2} + 6x - 7\\ 0 & = \left( {x + 7} \right)\left( {x - 1} \right)\hspace{0.25in} \Rightarrow \hspace{0.25in} x = - 7,\,\,\,\,\,x = 1\end{align*}\]The \(x\)-intercepts for this equation are then the two points : \(\left( { - 7,0} \right)\) and \(\left( {1,0} \right)\) .