# How do you find the x and y intercepts for y = -|x+10|?

Mar 29, 2018

General shape is $\bigwedge$

${y}_{\text{intercept}} \to \left(x , y\right) = \left(0 , - 10\right)$

${x}_{\text{intercept}} \to \left(x , y\right) = \left(10 , 0\right)$

Vertex $\to \left(x , y\right) = \left(- 10 , 0\right)$

#### Explanation:

$\textcolor{b l u e}{\text{Tip 1: Shape of the graph}}$

If an absolute is positive we get the shape $\bigvee$

If an absolute is negative we get the shape $\bigwedge \textcolor{red}{\leftarrow \text{ Our one}}$

This follows the same pattern as with a quadratic.

If the ${x}^{2}$ term is positive we get $\bigcup$

If the ${x}^{2}$ term is negative we get $\bigcap$
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$\textcolor{b l u e}{\text{Tip 2: horizontal position}}$

If you add a value to the $x$ then it moves the graph left
If you subtract a value from the $x$ then it moves the graph right

$y = {x}^{2} + 2 x - 2$
then we dicide to change it so that we add 4 to $x$. We have:

$y = {\left(x + 4\right)}^{2} + 2 \left(x + 4\right) - 2$

Because we have added 4 it moves the graph $y = {x}^{2} _ 2 x - 2$ left by 4

$\textcolor{red}{\text{Our one:}}$
So if we add 10 to $y = - | x |$ giving $y = - | x + 10 |$ we move the graph of $y = - | x |$ left by 10
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$\textcolor{b l u e}{\text{Tip 3: x-intercept}}$

The graph crosses the x-axis at $y = 0$

$y = - | x + 10 | \textcolor{w h i t e}{\text{d")-> color(white)("d}} 0 = - | x - 10 |$

The only way we can obtain 0 as the value of $y$ is if $x = + 10$

So we have: ${x}_{\text{intercept}} \to \left(x , y\right) = \left(10 , 0\right)$
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$\textcolor{b l u e}{\text{Tip 4: y-intercept}}$

The graph crosses the y-axis at $x = 0$

$y = - | 0 + 10 | = - 10$

So we have: ${y}_{\text{intercept}} \to \left(x , y\right) = \left(0 , - 10\right)$
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$\textcolor{b l u e}{\text{Tip 4: The vertex}}$

This occurs when the overall value $\textcolor{red}{\text{within}}$ the absolute is about to 'flip' sign from positive to negative. That is, it becomes 0 which happens at $x = - 10$

$y = - | \textcolor{m a \ge n t a}{x} + 10 |$

$\textcolor{\lim e g r e e n}{y} = - | \underbrace{\textcolor{m a \ge n t a}{- 10} + 10} | = \textcolor{\lim e g r e e n}{0}$
$\textcolor{w h i t e}{\text{ddddddddd}} \downarrow$
$\textcolor{w h i t e}{\text{dddddddd.d}} 0$

Vertex $\to \left(x , y\right) = \left(\textcolor{m a \ge n t a}{- 10} , \textcolor{\lim e g r e e n}{0}\right)$ 