introduction the formula for finding the area of a trapezoid, is a formula because it involves two...

Introduction

The formula for finding the area of a trapezoid,

is a formula because it involves two or

more variables that have specific and special

relationships with the other variables. In this case, the

formula involves four variables: b1, a base of the

trapezoid; b2, the other base of the trapezoid; h, the

height of the trapezoid; and A, the area of the trapezoid.

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5.3.4: Rearranging Formulas

IntroductionWhen you rearrange the formula, you are simply changing the focus of the formula. In its given form, the focus is A, the area. However, when it is necessary to find the height, h becomes the focus of the formula and thus is isolated using proper algebraic properties. In this lesson, you will rearrange literal equations (equations that involve two or more variables) and formulas with a degree of 2.

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Key Concepts• Literal equations and formulas contain equal signs.

• Just as in any other equation, we must apply proper algebraic properties to maintain a balance when changing the focus of an equation or formula. That is, if you subtract a value from one side of the equation, you must do the same to the other side, and so on.

• When you change the focus of a literal equation or formula, you are isolating the variable in question.

• To isolate a variable that is squared, perform the inverse operation by taking the square root of both sides of the equation.

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Key Concepts, continued• When you take the square root of a real number there

are two solutions: one is positive and the other is negative.

• Take (a)2, for example. When you square a, the result is a2. The same, however, is true for (–a)2.

• When you square –a, the result is still a2 because the product of two negatives is a positive. In other words, (–a)2 = a2.

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Key Concepts, continued• Since taking a square root involves finding a number

that you can multiply by itself to result in the square, we must take into account both the positive and negative.

• That is,

• When solving for a squared term of a formula, the focus is important in determining whether to use two solutions.

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Key Concepts, continued• If the focus is any quantity that would never be

negative in real life, such as distance, time, or population, it is appropriate to ignore the negative.

• When solving for a variable in a multi-step equation, first isolate the term containing the variable using subtraction or addition. Then determine which operations are applied to the variable, and undo them in reverse order.

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Common Errors/Misconceptions• forgetting to use the inverse operations in the correct

order • forgetting that there are likely two solutions (one

positive and one negative) when solving for a squared term

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Guided Practice

Example 1Solve the equation x2 + y2 = 100 for y.

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Guided Practice: Example 1, continued

1. Isolate y. Begin by subtracting x2 from both sides.

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x2 + y2 = 100 Original equation

y2 = 100 – x2 Subtract x2 from both sides.

Take the square root of both sides.

Simplify, remembering that the result could be positive or negative.


2. Summarize your result. The formula x2 + y2 = 100 can be rewritten as

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✔


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Guided Practice

Example 2Solve y = 3(x – 7)2 + 8 for x.

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1. Isolate x.

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y = 3(x – 7)2 + 8 Original equation

y – 8 = 3(x – 7)2 Subtract 8 from both sides.

Divide both sides by 3.

Simplify.


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Take the square root of both sides.

Simplify.

Add 7 to both sides.


2. Summarize your result.The equation y = 3(x – 7)2 + 8 solved for x is

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✔


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introduction the formula for finding the area of a trapezoid, is a formula because it involves two...

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