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Find the solutions for each absolute value equation:

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Presentation on theme: "Find the solutions for each absolute value equation:"— Presentation transcript:

1 Find the solutions for each absolute value equation:

2 Math 8H Graphing Absolute Value Equations Algebra 1 Glencoe McGraw-Hill JoAnn Evans

3 The ABSOLUTE VALUE of a real number is the distance between the origin and the point representing the real number. The number 5 is five spaces from 0, the origin. 0 is zero spaces from itself. The number -3 is three spaces from 0, the origin. Distance is not negative; the absolute value of a number will never be negative. |x| = x when x > 0 |x| = -x when x < 0 |0| = 0

4 Graph the equation: y = |x| x y Every absolute value equation will graph into a v-shape. The VERTEX is the point of the v-shaped graph. Some will open up, others will open down.

5 Graph y = -|x|Graph y = |x - 2| x y vertex x y How does this graph differ from y = |x|?

6 Graph y = |x| + 1Graph y = |x| - 3 x y vertex x y How does this graph differ from y = |x|?

7 Graph y = |x + 2|Graph y = |x - 1| x y vertex x y How does this graph differ from y = |x|?

8 It’s possible to tell what the x value of the vertex will be just by looking at the absolute value equation. Why is this useful information Knowing the x-value of the vertex will help you to efficiently select x-values for the table of values. You need several values on either side of the vertex in order to see the v-shape appear. The value of x that will make the expression INSIDE the absolute value symbol equal to ZERO will be the x-value of the vertex of the graph.

9 To Sketch the Graph of an Absolute Value Equation: 1.Find the value of x that will make the expression inside the absolute value symbol equal to zero. Place this value of x in the middle of your table of values. 2.Choose two values of x less than this number and two values of x greater than this number. 3.Calculate the corresponding y values and sketch the resulting v-shaped graph. If the x values are evenly spaced on either side of the x value of the vertex, the y values should show a pattern.

10 Sketch the graph of y = |x + 2| y x is the x value of the vertex. Place it in the middle of the table. Choose 2 values less and 2 values more, evenly spacing them. What value of x will make the expression inside the absolute value sign equal to 0?

11 Sketch the graph of y = -2|x - 1| When there’s a negative coefficient before the absolute value symbol, the graph will open down. What value of x will make the expression inside the absolute value sign equal to 0? y x Place 1 in the middle of the table. Choose 2 values less and 2 values more, evenly spaced.

12 Sketch the graph of When there’s a positive coefficient before the absolute value symbol, the graph will open up. -2 What value of x will make the expression inside the absolute value sign equal to 0? y x Place -2 in the middle of the table. Choose 2 values less and 2 values more, evenly spaced.

13 Is there a way to easily tell what the y value of the vertex will be? y = |x| + 1What will the x value of the vertex be? If x is 0, what is y? 0 1 y = |x - 2| - 5 What will the x value of the vertex be? If x is 2, what is y? 2 -5 y = |x + 3| - 4 What will the x value of the vertex be? If x is -3, what is y? y = 2|x - 1| + 7 What will the x value of the vertex be? If x is 1, what is y? 7 1

14 What will be the coordinates of the vertex? y = |x| + 3 y = |x + 8| y = |x| - 5 y = |x + 9| - 14 y = -5|x + 2| y = 2|2x – 4| + 6 y = -|x – 1| + 5 (0, 3) (-8, 0) (0, -5) (-9, -14) (-2, 0) (2, 6) (1, 5)


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