Math Problem Statement
Solution
To find the vertex of the function , we analyze the form of an absolute value function.
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The function is given by:
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The general form of an absolute value function is: where represents the vertex of the function.
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In , we can rewrite it as: This shows that and .
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Therefore, the vertex of this absolute value function is located at:
Answer: The coordinates of the vertex are .
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Related Questions
- How do you determine the vertex of a general absolute value function?
- What effect does changing the coefficient of the absolute value term have on the graph?
- How would the graph shift if we added a constant term to ?
- What would the graph look like if the absolute value term had a negative coefficient?
- How does the slope of the lines formed in an absolute value graph relate to the coefficient outside the absolute value?
Tip:
Remember, the vertex of an absolute value function is always at the point , where shifts the graph horizontally and shifts it vertically.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Functions
Vertex Form of Absolute Value Functions
Formulas
Vertex form of an absolute value function f(x) = a|x - h| + k
Theorems
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Suitable Grade Level
Grades 7-10
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