Math Problem Statement

Fill in the equation for the graph y = |x - [?]| + [ ] based on the given absolute value graph.

Solution

This graph represents a V-shaped absolute value function. The general form for such a function is:

y=xh+ky = |x - h| + k

Where (h,k)(h, k) is the vertex of the graph. The vertex in this graph appears to be at (2,0)(2, 0), 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:

y=x2y = |x - 2|

Thus, for the blanks in the equation:

  1. The first blank (inside the absolute value) should be 2.
  2. The second blank (outside the absolute value) is 0 since there's no vertical shift.

The final equation is:

y=x2+0y = |x - 2| + 0

Would you like further details or have any other questions about this equation or graph?

Here are some related questions for you:

  1. How do you determine the vertex of an absolute value function from its graph?
  2. What happens to the graph when we change the values of hh and kk in y=xh+ky = |x - h| + k?
  3. How would the graph change if the function was y=x+2y = |x + 2| instead?
  4. How does a reflection over the x-axis affect the equation of an absolute value function?
  5. 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