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How To Create an Absolute Value Graph

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Jana Russick
March 24, 2021

Absolute value graphs are linear representations of absolute value functions. These equations are always expressed within absolute value bars. Here is an example: Taking the absolute value of a number or equation cancels out its negative signs. Even though there is a -1 in the equation above, the x-intercept would be (1,0) since anything within absolute value bars becomes positive.

When graphing absolute value equations, the shape will either be an upright or upside-down V. The point where the "V" meets represents the vertex of the graph. Let's create a graph of the absolute value function above: From this graph, we can determine that the vertex of this equation is (1,0), the y-intercept is (0,2), and the graph opens upward.

Breaking Down Absolute Value Functions

Let's explain the rules of absolute value functions. The parent function, or the most basic form, of an absolute value, is:  The general form of an absolute value function is as follows: Here’s what we can learn from this form:

• The vertex of this equation is at points (h, k).
• The horizontal axis of symmetry is marked where x = h.
• The variable k determines the vertical distance from 0.
• Whether a is positive or negative determines if the graph opens up or down.

Analyzing an Absolute Value Graph

Let's analyze the graph of an absolute value function f to determine its vertex, x-intercepts, and whether it opens up or down.   From this equation, we can determine that the vertex is (-4, 3). Because a = -2, the graph opens down. The x-intercepts are -5.5 and -3.5, and the y-intercept is -5.

Understanding Absolute Value Graphs

The absolute value of a number represents its distance from 0. Graphing absolute value equations allows us to visually understand this concept in terms of x and y-intercepts. It also teaches us how to determine the vertex of an absolute value function and whether it will be upward or downward-facing.

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