10 Pull It All Together

BIG idea Equivalence

Radical expressions can be represented many ways. To simplify a square root, factor out perfect squares from the radicand.

Task 1

Use the isosceles right triangle shown to answer the following questions.

1. What is an expression for c in terms of x? Write your answer as a radical in simplified form.
2. How can you use your result from part (a) to find the length of the hypotenuse of an isosceles right triangle if you know the length of each leg?

BIG idea Functions

Square root functions contain a variable in the radicand. The parent square root function is y   =   x . y equals square root of x .

Task 2

Solve. Show your work.

1. Graph the function y = | x | . y equals , square root of absolute value of x , end root . .
2. How does the graph of the function in part (a) differ from the graph of the parent square root function y = x ? y equals square root of x , question mark
3. What are the domain and range of the function in part (a)?

BIG idea Solving Equations and Inequalities

To isolate the variable in a radical equation, first isolate the radical, and then square both sides.

Task 3

Solve. Show all your work and explain your steps.

The distance d in feet of a certain projector from a screen is given by d = 1.2 A , d equals 1.2 , square root of eh . comma  where A is the area of the projector's image in square feet. Suppose you move the projector from its current position 8 ft from the screen to a new position 12 ft from the screen. By how much does the area of the image increase?

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