Example 2 A Isolate the absolute value expression in each equation to determine if the equation can be solved. Geometry Find the points where a circle centered at 3, 0 with a radius of 5 crosses the x-axis. Write yes or no for each number in the table. Also, if a is negative, then the graph opens downward, instead of upwards as usual. Analyze Information Identify the important information. Terry is trying to place a satellite dish on the roof of his house at the recommended height of 30 feet.

NextNow plot the three points and graph g x. It is reflected off a mirror on the floor that is 15 feet from the wall the light originates from. The x-coordinate will be reflected in the y-axis and of , then moved units to the The y-coordinate will move So, 2, 2 becomes becomes , unit. You are playing a history quiz game where you must give the years of historical events. Graph the solutions on a number line. To graph an absolute-value function, choose several values of x and generate some ordered pairs Have students substitute in x values inputs into the equation and solve for the y values outputs. Justify Your Reasoning This absolute value equation has nested absolute values.

NextOn average, a squirrel lives to be 6. What is the range of answers that allow you to score points? Again, the best way to illustrate this simple idea is through the use of examples! Is it possible for an absolute value equation to have no solutions? In order to score any points at all for a question about the year in which a man first stepped on the moon, your answer must be no more than 3 years away from the correct answer, 1969. Imagine that a coordinate plane is placed over a side of the building. Here, you will explore what happens when you solve absolute value inequalities. Essential Question Check-In Describe, in your own words, the basic steps to solving absolute value equations and how many solutions to expect.

NextFocus on Higher Order Thinking 19. Evaluate g © Houghton Mifflin Harcourt Publishing Company Solve The vertex of g x is at Evaluate g x at Substitute. The player is going to bank the ball off the side wall of the green at 6, 8. Independent Practice Have students work through independent practice. Imagine that a coordinate plane is placed over the pool table.

NextModule 2 76 Lesson 3 Evaluate: Homework and Practice 1. In this case, only the x is inside the absolute-value bars. However, because of how absolute values behave, it is important to include negative inputs in your T-chart when graphing absolute-value functions. A box of cereal is supposed to weigh 13. If one student bounce-passes the ball from a height of 1. Purplemath Taking the of a negative number makes it positive. Example 2 A Solve the inequality algebraically.

NextWhen the absolute value is equal to a negative number, there is no solution because absolute value is never negative. Explain 1 Solving Absolute Value Inequalities Graphically Example 1 A Solve the inequality graphically. Match each graph with its function. What is the range of typical speeds on this road? Calculate the percentage variation variation divided by average distance in the orbit of each of the planets. Graph the solution on a number line. © Houghton Mifflin Harcourt Publishing Company 6.

NextMulti-Step A golf player is trying to make a hole-in-one on the miniature golf green shown. Now plot the three points and use them to sketch g x. A rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. Graph the solutions on a number line. Lesson 3 Your Turn Solve the inequality algebraically. The x-coordinate of each point will be shifted 5 units to the right while the y-coordinate will be stretched by a factor of 4 and then moved down 2 units. Write and solve an absolute value inequality to find the range of acceptable weights.

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