Math Problem Statement
Solution
This graph represents a V-shaped absolute value function. The general form for such a function is:
Where is the vertex of the graph. The vertex in this graph appears to be at , meaning the function is shifted 2 units to the right along the x-axis and does not have any vertical shift (it remains on the x-axis).
So, the equation of this graph is:
Thus, for the blanks in the equation:
- The first blank (inside the absolute value) should be 2.
- The second blank (outside the absolute value) is 0 since there's no vertical shift.
The final equation is:
Would you like further details or have any other questions about this equation or graph?
Here are some related questions for you:
- How do you determine the vertex of an absolute value function from its graph?
- What happens to the graph when we change the values of and in ?
- How would the graph change if the function was instead?
- How does a reflection over the x-axis affect the equation of an absolute value function?
- What are the general characteristics of the graph of an absolute value function?
Tip: Always look for the vertex (the "V" point) when identifying the equation of an absolute value function! It tells you both the horizontal and vertical shifts.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Functions
Graph Shifting
Algebra
Formulas
y = |x - h| + k
Theorems
Vertex form of absolute value functions
Suitable Grade Level
Grades 8-10
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