Solving and Graphing Radical Functions Skill 26 ObjectivesVocabulary

Solving and Graphing Radical Functions Skill 26

Objectives/Vocabulary Students will be able to: Understand the basics of radical equations and solving radical equations Key Vocabulary: Radical Equation Extraneous Square Roots Root

Radical Equation A Radical Equation is an equation in which the variable is under the radical symbol i. e. the variable is the radicand.

Steps to Solve a Radical Equation 1. Isolate the radical (or one of the radicals if there is more than one) to one side of the equation. 2. Square both sides of the resulting equation if the radical is a square root. Otherwise raise both sides to the power equal to the index of the radical. 3. Solve the resulting equation for the variable. 4. Check all the answers you get by putting them in the original equation to avoid extraneous roots (which are not a part of solution).

Examples: Solve the Radical Equation

Examples: Solve the Radical Equation

Examples: Radical Equations with Extraneous Roots The roots of a radical equation which do not satisfy the radical equation are known as the extraneous roots.

Solve Other Radical Equation For solving radical equations having radical other than a square root, the steps are the same except both sides of the equation are raised the same power as the index of the radical. Remember! Odd denominator in the index One solution with + sign Even denominator in the index

Examples: Solve the Radical Equation

Examples: Solve the Radical Equation c) The roots of the radical equation not satisfying the radical equation are known as: i. Extraneous Roots ii. Extra Roots iii. Complex Roots iv. Real Roots

Examples: Solve the Radical Equation

Graphing Square Root & Other Radicals

Cube Root Graph

Fourth Root Graph

Transforming Radical Graphs

Examples: Graph the Radical Function

Examples: Graph the Radical Function

Examples: Graph the Radical Function

Solving Radical Equations Questions? Packet Skill 26 Prepare for your quiz
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