Translating 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 = a|x - h| + k, where (h, k) is the vertex of the graph.

Front

How does the value of 'a' affect the graph of an absolute value equation?

Back

The value of 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph is stretched; if 0 < |a| < 1, the graph is compressed.

Front

What does the expression |x - h| represent in an absolute value equation?

Back

The expression |x - h| represents the horizontal shift of the graph. 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 adding a constant 'k' to the absolute value equation?

Back

Adding a constant 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What are the coordinates of the vertex in the equation y = a|x - h| + k?

Back

The coordinates of the vertex are (h, k).

Front

How do you determine the vertex from the equation y = |x + 3| - 5?

Back

The vertex can be determined by identifying h and k. Here, h = -3 and k = -5, so the vertex is (-3, -5).

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 its vertex at the origin (0, 0).

Front

How does the equation y = |x| + 2 differ from y = |x|?

Back

The equation y = |x| + 2 shifts the graph of y = |x| up by 2 units.

Front

What is the significance of the vertex in an absolute value graph?

Back

The vertex is the point where the graph changes direction and represents the minimum or maximum value of the function.

Front

How do you find the x-intercepts of the equation y = |x - 2|?

Back

To find the x-intercepts, set y = 0: 0 = |x - 2|, which gives x = 2.