College Algebra, Chapter 2, 2.2, Section 2.2, Problem 42

Find the $x$ and $y$ intercept of $\displaystyle y = x^2 - 5x + 6$


$
\begin{equation}
\begin{aligned}

y =& x^2 - 5x + 6
&& \text{Given}
\\
\\
y =& (x - 3)(x - 2)
&& \text{Factor}

\end{aligned}
\end{equation}
$


To solve for $y$ intercept, we set $x = 0$


$
\begin{equation}
\begin{aligned}

y =& (0 -3)(0 - 2)
\\
\\
y =& (-3)(-2)
\\
\\
y =& 6

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0,6)$

To solve for $x$ intercept, we set $y =0$


$
\begin{equation}
\begin{aligned}

0 =& (x - 3)(x - 2)
&& \text{Zero Product Property}
\\
\\
0 =& x - 3 \text{ and } 0 = x - 2
&& \text{Solve for } x
\\
\\
x =& 3 \text{ and } x = 2
&&

\end{aligned}
\end{equation}
$


Thus, the $x$ intercepts are at $(3,0)$ and $(2, 0)$