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

How 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

What effect does the '-4' have in the equation y = |x| - 4?

Back

The '-4' shifts the graph of y = |x| downwards by 4 units.

Front

What does the expression |x - 3| represent in the equation y = |x - 3| - 1?

Back

The expression |x - 3| represents the distance of x from 3 on the number line.

Front

What is the vertex of the graph for the equation y = |x - 3| - 1?

Back

The vertex of the graph is at the point (3, -1).

Front

How does the '+1' affect the graph of y = |x| + 1?

Back

The '+1' shifts the graph of y = |x| upwards by 1 unit.

Front

What is the significance of the absolute value in the equation y = |x + 1| - 4?

Back

The absolute value ensures that the output is always non-negative, representing the distance from the line x = -1.

Front

What does the graph of y = |x - 3| look like?

Back

The graph of y = |x - 3| is a V-shape with the vertex at (3, 0) and opens upwards.

Front

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

Back

Set y = 0: |x| - 4 = 0, which gives x = 4 and x = -4 as the x-intercepts.

Front

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

Back

A negative coefficient reflects the graph of the absolute value function across the x-axis.