2.8 Absolute Value Functions
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1 2.8 Absolute Value Functions Algebra III Mr. Niedert Algebra III 2.8 Absolute Value Functions Mr. Niedert 1 / 8
2 Today s Learning Target(s) 1 I can graph absolute value functions and apply them to real-life situations. Algebra III 2.8 Absolute Value Functions Mr. Niedert 2 / 8
3 Absolute Value Functions Absolute value functions have the form y = a x h + k. Algebra III 2.8 Absolute Value Functions Mr. Niedert 3 / 8
4 Absolute Value Functions Absolute value functions have the form y = a x h + k. The function is V-shaped, but can also be flipped over to make an upside down V. Algebra III 2.8 Absolute Value Functions Mr. Niedert 3 / 8
5 Absolute Value Functions Absolute value functions have the form y = a x h + k. The function is V-shaped, but can also be flipped over to make an upside down V. If a > 0, then the function will look like a normal V. Algebra III 2.8 Absolute Value Functions Mr. Niedert 3 / 8
6 Absolute Value Functions Absolute value functions have the form y = a x h + k. The function is V-shaped, but can also be flipped over to make an upside down V. If a > 0, then the function will look like a normal V. If a < 0, then the function will be upside down. Algebra III 2.8 Absolute Value Functions Mr. Niedert 3 / 8
7 Absolute Value Functions Absolute value functions have the form y = a x h + k. The function is V-shaped, but can also be flipped over to make an upside down V. If a > 0, then the function will look like a normal V. If a < 0, then the function will be upside down. The vertex of the absolute value function is the point (h, k). Algebra III 2.8 Absolute Value Functions Mr. Niedert 3 / 8
8 Absolute Value Functions Absolute value functions have the form y = a x h + k. The function is V-shaped, but can also be flipped over to make an upside down V. If a > 0, then the function will look like a normal V. If a < 0, then the function will be upside down. The vertex of the absolute value function is the point (h, k). The vertical line through the vertex has the equation x = h and is referred to as the axis of symmetry. Algebra III 2.8 Absolute Value Functions Mr. Niedert 3 / 8
9 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
10 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
11 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). 2 Identify the value of a. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
12 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). 2 Identify the value of a. If it is positive, the V will open upwards. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
13 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). 2 Identify the value of a. If it is positive, the V will open upwards. If it is negative, the V will open downwards. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
14 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). 2 Identify the value of a. If it is positive, the V will open upwards. If it is negative, the V will open downwards. 3 Use the value of a as the slope of the right branch to find the second point. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
15 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). 2 Identify the value of a. If it is positive, the V will open upwards. If it is negative, the V will open downwards. 3 Use the value of a as the slope of the right branch to find the second point. 4 Reflect that point over the axis of symmetry to find your third point. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
16 Graphing an Absolute Value Function Graphing an Absolute Value Function Use the following steps to help guide you when graphing absolute value functions. 1 Identify h and k, and use this to graph the vertex at (h, k). 2 Identify the value of a. If it is positive, the V will open upwards. If it is negative, the V will open downwards. 3 Use the value of a as the slope of the right branch to find the second point. 4 Reflect that point over the axis of symmetry to find your third point. 5 Connect the three points so that you have a V-shaped function. Algebra III 2.8 Absolute Value Functions Mr. Niedert 4 / 8
17 Graphing an Absolute Value Function Example Graph y = x 2 5. Algebra III 2.8 Absolute Value Functions Mr. Niedert 5 / 8
18 Graphing an Absolute Value Function Practice Graph y = x Algebra III 2.8 Absolute Value Functions Mr. Niedert 6 / 8
19 Writing an Absolute Value Function Practice Write an equation for the graph below. Algebra III 2.8 Absolute Value Functions Mr. Niedert 7 / 8
20 2.8 Absolute Value Functions Assignment pg #12-17, even, Algebra III 2.8 Absolute Value Functions Mr. Niedert 8 / 8
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