Examples of Student Work at this Level The student correctly writes and solves the first equation: A difference is described between two values. This is the solution for equation 2. Sciencing Video Vault 1. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.
Equation 2 is the correct one.
Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? If needed, clarify the difference between an absolute value equation and the statement of its solutions.
Writes the solutions of the first equation using absolute value symbols.
Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? Evaluate the expression x — 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and Emphasize that each expression simply means the difference between x and Ask the student to solve the equation and provide feedback.
What is the difference? For a random number x, both the following equations are true: Then explain why the equation the student originally wrote does not model the relationship described in the problem.
If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. For example, represent the difference between x and 12 as x — 12 or 12 — x. Instructional Implications Model using absolute value to represent differences between two numbers.
To solve this, you have to set up two equalities and solve each separately. Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i.
Guide the student to write an equation to represent the relationship described in the second problem. Should you use absolute value symbols to show the solutions? Finds only one of the solutions of the first equation. Got It The student provides complete and correct responses to all components of the task.
Set Up Two Equations Set up two separate and unrelated equations for x in terms of y, being careful not to treat them as two equations in two variables: Instructional Implications Provide feedback to the student concerning any errors made. You can now drop the absolute value brackets from the original equation and write instead: This means that any equation that has an absolute value in it has two possible solutions.
Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.
Provide additional opportunities for the student to write and solve absolute value equations.The other case for absolute value inequalities is the "greater than" case.
Let's first return to the number line, and consider the inequality | x | > The solution will be all. For absolute value equations multiplied by a constant (for example, y = a | x |),if 0 1, it is stretched. Also, if a is negative, then the graph opens downward, instead of upwards as usual.
Absolute Value Functions To graph an absolute value function you may find it helpful to plot the vertex and one other point.
Use symmetry to plot a third point and then complete the graph. Writing an Absolute Value Function Write an equation of the graph shown. SOLUTION The vertex of the graph is (0, º3), so the equation has the form.
The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions. While absolute-value graphs tend to look like the one above, with an "elbow" in the middle, this is not always the case.
However, if you see a graph with an elbow like this, you should expect that the equation is probably an absolute value. You can denote absolute value by a pair of vertical lines bracketing the number in question. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.Download