# How do you graph  y = abs(4x + 2 ) + 3?

May 1, 2016

$y \ge 3$. Draw the straight lines $y = 3 , y = 4 x + 5 \mathmr{and} y = - 4 x + 1$.
Sans the parts below the point of intersection (-1/2, 3), the 2nd and 3rd form the graph, for the given equation.

#### Explanation:

Importantly, $y \ge 3$.

The given equation is the combined equation for the separate equations

$y = \left(4 x + 2\right) + 3 \mathmr{and} y = - \left(4 x + 2\right) + 3$.. Simplified, these are

$y = 4 x + 5 \mathmr{and} y = - 4 x + 1$

that represent two straight lines meeting at ( -1/2, 3).

Draw the straight lines $y = 4 x + 5 \mathmr{and} y = - 4 x - 1$.

Sans the parts below the common point, the 2nd and 3rd form the
graph, for the given equation.