Graphing Absolute Value Equations

Front

What is the general form of an absolute value equation?

Back

The general form of an absolute value equation is y = |x - h| + k, where (h, k) is the vertex of the graph.

Front

What does the vertex of the graph of an absolute value function represent?

Back

The vertex represents the minimum or maximum point of the graph, depending on the orientation.

Front

How does the value of 'k' affect the graph of y = |x - h| + k?

Back

The value of 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

How does the value of 'h' affect the graph of y = |x - h| + k?

Back

The value of 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of a negative sign in front of the absolute value, such as in y = -|x|?

Back

A negative sign in front of the absolute value reflects the graph across the x-axis.

Front

What is the solution to the equation y = |x - 2| + 3 when y = 5?

Back

To solve |x - 2| + 3 = 5, subtract 3 from both sides to get |x - 2| = 2. The solutions are x = 4 and x = 0.

Front

What is the solution to the equation y = |x| - 2 when y = 0?

Back

To solve |x| - 2 = 0, add 2 to both sides to get |x| = 2. The solutions are x = 2 and x = -2.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards with the vertex at the origin (0,0).

Front

How do you find the x-intercepts of the equation y = |x + 1| - 4?

Back

To find the x-intercepts, set y = 0: |x + 1| - 4 = 0. This gives |x + 1| = 4, leading to x = 3 and x = -5.

Front

What is the significance of the absolute value in an equation?

Back

The absolute value ensures that the output is always non-negative, representing distance from zero.