Download presentation

Presentation is loading. Please wait.

Published byGabrielle Burton Modified over 2 years ago

1
Warm Up Find the solutions for each absolute value equation:

2
**Graphing Absolute Value Equations**

Math 8H Graphing Absolute Value Equations Algebra 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. |x| = x when x > 0 0 is zero spaces from itself. |0| = 0 The number -3 is three spaces from 0, the origin. |x| = -x when x < 0 Distance is not negative; the absolute value of a number will never be negative.

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
**How does this graph differ from y = |x|?**

Graph y = -|x| Graph y = |x - 2| How does this graph differ from y = |x|? How does this graph differ from y = |x|? x y x y -2 -1 1 2 -2 -1 -2 2 4 6 4 2 vertex vertex

6
**How does this graph differ from y = |x|? **

Graph y = |x| + 1 Graph y = |x| - 3 How does this graph differ from y = |x|? How does this graph differ from y = |x|? x y x y -2 -1 1 2 3 2 1 -2 -1 1 2 -1 -2 -3 vertex vertex

7
**How does this graph differ from y = |x|? **

Graph y = |x + 2| Graph y = |x - 1| How does this graph differ from y = |x|? How does this graph differ from y = |x|? x y x y -4 -3 -2 -1 2 1 -1 1 2 3 2 1 vertex vertex

8
**Why is this useful information**

It’s possible to tell what the x value of the vertex will be just by looking at the absolute value equation. 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. 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.

9
**To Sketch the Graph of an Absolute Value Equation:**

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. Choose two values of x less than this number and two values of x greater than this number. 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
**-2 Sketch the graph of y = |x + 2| - 3**

What value of x will make the expression inside the absolute value sign equal to 0? -2 x y -4 -3 -2 -1 -1 -2 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. -2 -3 -2 -1

11
**What value of x will make the expression inside the absolute value sign equal to 0?**

Sketch the graph of y = -2|x - 1| + 2 x y 1 -1 1 2 3 -2 Place 1 in the middle of the table. Choose 2 values less and 2 values more, evenly spaced. 2 -2 When there’s a negative coefficient before the absolute value symbol, the graph will open down.

12
**What value of x will make the expression inside the absolute value sign equal to 0?**

Sketch the graph of x y -2 -4 -3 -2 -1 -2 Place -2 in the middle of the table. Choose 2 values less and 2 values more, evenly spaced. -2.5 -3 -2.5 -2 When there’s a positive coefficient before the absolute value symbol, the graph will open up.

13
**Is there a way to easily tell what the y value of the vertex will be?**

y = |x| + 1 What will the x value of the vertex be? 1 If x is 0, what is y? y = |x - 2| - 5 What will the x value of the vertex be? 2 -5 If x is 2, what is y? y = |x + 3| - 4 -3 What will the x value of the vertex be? -4 If x is -3, what is y? 1 y = 2|x - 1| + 7 What will the x value of the vertex be? 7 If x is 1, what is y?

14
**What will be the coordinates of the vertex?**

(0, 3) (-8, 0) (0, -5) (-9, -14) (-2, 0) (2, 6) (1, 5) 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

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on iso 9000 and 14000 Ppt on fire extinguisher types for servers Ppt on current account deficit india Ppt on central limit theorem explained Poster templates free download ppt on pollution Ppt on polynomials in maths what does commutative mean Ppt on biodegradable and non biodegradable Ppt on job evaluation systems Ppt on fuel cell Ppt on adivasis of india