# Question #60683

Jul 1, 2015

(note: $y$ is equivalent to $p \left(x\right)$ for this question)
y-intercept $= 6$
x-intercepts $= - 2 \mathmr{and} - 3$

#### Explanation:

The y-intercept is the value of y (or as in the question $p \left(x\right)$ where the graph of the equation crosses the y-axis. This is the point on the graph where $x = 0$ (since $x = 0$ for all points on the y-axis).
$\textcolor{w h i t e}{\text{XXXX}}$$y = {\left(0\right)}^{2} + 5 \left(0\right) + 6 = 6$

The x-intercepts similarly are the values of $x$ when $y$ (or $p \left(x\right)$) $= 0$
$\textcolor{w h i t e}{\text{XXXX}}$$0 = {x}^{2} + 5 x + 6$

$\textcolor{w h i t e}{\text{XXXX}}$$\left(x + 2\right) \left(x + 3\right) = 0$

$\textcolor{w h i t e}{\text{XXXX}}$$\Rightarrow x = - 2$
$\textcolor{w h i t e}{\text{XXXX}}$or $x = - 3$