# How do you find the x and y intercepts for f(x)=x^2-9x+14?

Jan 20, 2016

y-intercept: $14$
x-intercepts: $2$ and $7$

#### Explanation:

Note that $y$ is equivalent to $f \left(x\right)$
So we can think of the given equation as
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 9 x + 14$

The y-intercept is the value of $y$ when $x = 0$.
Given the form of the equation above, clearly:
$\textcolor{w h i t e}{\text{XXX}}$y-intercept $= 14$

The x-intercept(s) is/are the value(s) of $x$ for which $y = 0$
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 9 x + 14 = 0$

$\rightarrow \textcolor{w h i t e}{\text{X}} \left(x - 7\right) \left(x - 2\right) = 0$

That is $x = 7$ or $x = 2$

$\textcolor{w h i t e}{\text{XXX}}$x-intercepts: $= 7$ and $2$