Algebra 2 / Unit 1: Functions and Transformations
1.4 Absolute Value Functions
Notes
The graph of $y = a|x - h| + k$ is a V with vertex $(h, k)$.
- If $a > 0$ the V opens up (vertex is a minimum). If $a < 0$ it opens down (vertex is a maximum).
- The two sides have slopes $a$ and $-a$.
- To find $x$-intercepts, set $y = 0$ and solve the absolute value equation.
- Example: $y = |x - 2| - 5$: $|x - 2| = 5$, so $x = 7$ or $x = -3$.
Practice
What is the vertex of $y = -2|x + 3| + 7$?
$x + 3 = x - (-3)$, so $h = -3$ and $k = 7$.
What are the $x$-intercepts of $y = |x - 2| - 5$?
$|x - 2| = 5$ gives $x - 2 = 5$ or $x - 2 = -5$.
Solve $|x - 4| < 3$.
"Less than" means between: $-3 < x - 4 < 3$, then add 4.
Ready for more? Take the Unit 1 test.