Writing Absolute Value Equations from Graphs

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shaped graph that opens upwards if the coefficient of the absolute value is positive and downwards if it is negative.

Front

What is the vertex of an absolute value function?

Back

Front

How does the coefficient of the absolute value affect the graph?

Back

The coefficient (a) affects the steepness of the graph. If |a| > 1, the graph is steeper; if 0 < |a| < 1, the graph is wider.

Front

What does a negative coefficient in front of the absolute value indicate?

Back

A negative coefficient indicates that the graph opens downwards, creating a maximum point at the vertex.

Front

How do you find the equation of an absolute value function from its graph?

Back

Front

What is the effect of a vertical shift on the graph of an absolute value function?

Back

A vertical shift moves the graph up or down. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of a horizontal shift on the graph of an absolute value function?

Back

A horizontal shift moves the graph left or right. If h is positive, the graph shifts right; if h is negative, it shifts left.

Front

How do you determine the slope of the lines in an absolute value function?

Back

Front

What is the significance of the y-intercept in an absolute value function?

Back

The y-intercept is the point where the graph crosses the y-axis, which can be found by substituting x = 0 into the equation.