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Square Root Functions

October 11th, 2011

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This just in

We have worked with Radicals in the form of SQUAREROOTS, and those with higher root powers!

GOOD NEWS: We only have to think about the SquareRoot Function!!

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Remember Inverse?

The Inverse of a Second-Degree Polynomial Functioncorresponds to a relation defined by two square root

functions.

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The Concept

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Law of Square Roots

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Law of Square Roots

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This is rationalizing thedenominator!

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The Basic Square RootFunctionMiss Connell

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Ordered Pairs

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Visuals

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Take a few minutes to check the

parameters with your graphingcalculator:

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The TransformedSquare Root FunctionMiss Connell

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The TransformedSquare Root FunctionMiss Connell

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So.

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Critical Thinking

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Reflection about the y-axis

They set the starting point

(or end point)

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Zeros and Equations

Square Root Functions

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Steps for Finding Zeros

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Example 1

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Example 2

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Example 3

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Example 3

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Sign

To determine the sign of a square root function:

1. Draw a graph using the coordinates of the vertex and thezero, if it exists

2. Read the intervals of the domain located on either side ofthe x-axis.

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Inequalities

Square Root Function

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Graphically

1. Determine where the two curves intersect, if applicable

2. Determine the interval(s) of the domain over which theimages of the first function are greater or less than thoseof the second, based on the given inequality.

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Algebraically

1. Find an inequality in which one of the two sides consistsof a radical

2. Comparing the inequality obtained with the positiverestriction of the radical, find the inequality (orinequalities) to be solved

3. Complete the solution to the inequality (or inequalities)

4. State the Solution Set.

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Algebraic Example

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Algebraic Example

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Finding the Rule

Square Root Function

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Old Text Page 113

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Old Text Page 113

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Example

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INVERSE

The inverse of a square root function is a restrictedquadratic function

HALF OF IT!

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Properties

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Practice

Page 105 #2bdfh, 3cd, 4, 5, 6, 8, 9, 10ad,11 (graph a,c,e using your calculator, and d,b,f without)

18, 19

Page 115 #3, 4, 5, 10, 13, 14, 21, 22a, 25, 28,

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