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  1. General form of an absolute value equation: f ( x) = a | x h | + k. The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h and k tell us how far the graph shifts horizontally and vertically. Some examples: Graph of y=|x|. Graph of y=3|x|. Graph of y=-|x|. Graph of y=|x+3|-2.

  2. 5 maj 2020 · Learn how to graph absolute value functions in this video math tutorial by Mario's Math Tutoring. We discuss how to graph the parent function as well as the transformations of the form...

  3. To solve absolute value equations, find x values that make the expression inside the absolute value positive or negative the constant. To graph absolute value functions, plot two lines for the positive and negative cases that meet at the expression's zero.

  4. Solving an Absolute Value Equation. Now that we can graph an absolute value function, we will learn how to solve an absolute value equation. To solve an equation such as \(8=|2x−6|\), we notice that the absolute value will be equal to 8 if the quantity inside the absolute value is 8 or -8.

  5. 23 mar 2024 · The Equality Properties can be proved using Equation \( \ref{AbsValDefn} \) and by looking at the cases when \(x \geq 0\), in which case \(|x| = x\), or when \(x < 0\), in which case \(|x| = -x\). For example, if \(c > 0\), and \(|x| = c\), then if \(x \geq 0\), we have \(x = |x| = c\).

  6. 21 wrz 2023 · To solve an absolute value equation, such as \(|X| = p\), replace it with the two equations \(X = −p\) and \(X = p\) and then solve each as usual. Absolute value equations can have up to two solutions.

  7. This topic covers: - Solving absolute value equations - Graphing absolute value functions - Solving absolute value inequalities

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