Lesson 32 Solving Radical Equations Math 2 Honors

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Lesson 32 – Solving Radical Equations Math 2 Honors - Santowski 12/27/2021 Math 2

Lesson 32 – Solving Radical Equations Math 2 Honors - Santowski 12/27/2021 Math 2 Honors - Santowski 1

Lesson Objectives n solutions to radical equations can be graphically or algebraically presented n

Lesson Objectives n solutions to radical equations can be graphically or algebraically presented n what do we mean by “equivalent” systems, why do they arise, and what do they mean, and why are they important n incorporate the idea that root functions have restrictions 12/27/2021 Math 2 Honors - Santowski 2

(A) Solving Radical Equations – Example #1 n We will investigate the idea of

(A) Solving Radical Equations – Example #1 n We will investigate the idea of “equivalent systems” n Use a graph to solve the equation n Explain what is meant by “equivalent systems” given your 2 solutions to the 2 equations 12/27/2021 Math 2 Honors - Santowski 3

(A) Solving Radical Equations – Example #1 n Algebraically solve 12/27/2021 Math 2 Honors

(A) Solving Radical Equations – Example #1 n Algebraically solve 12/27/2021 Math 2 Honors - Santowski 4

(A) Solving Radical Equations – Example #1 n Graphic solution is: n Equivalent system:

(A) Solving Radical Equations – Example #1 n Graphic solution is: n Equivalent system: 12/27/2021 n Algebra solution is: Math 2 Honors - Santowski 5

(B) Solving Radical Equations – Example #2 n We will investigate the idea of

(B) Solving Radical Equations – Example #2 n We will investigate the idea of “equivalent systems” n Use a graph to solve the equation n Is this an example of “equivalent systems” given your 2 solutions to the 2 equations? 12/27/2021 Math 2 Honors - Santowski 6

(B) Solving Radical Equations – Example #2 n Algebraically solve 12/27/2021 Math 2 Honors

(B) Solving Radical Equations – Example #2 n Algebraically solve 12/27/2021 Math 2 Honors - Santowski 7

(B) Solving Radical Equations – Example #2 n And the algebraic solution n Explain

(B) Solving Radical Equations – Example #2 n And the algebraic solution n Explain what the term “extraneous solution” means Explain WHY they occur. n 12/27/2021 Math 2 Honors - Santowski 8

(C) Solving Radical Equations – Example #3 n We will investigate the idea of

(C) Solving Radical Equations – Example #3 n We will investigate the idea of “equivalent systems” n Use a graph to solve the equation n Is this an example of “equivalent systems” given your 2 solutions to the 2 equations? 12/27/2021 Math 2 Honors - Santowski 9

(C) Solving Radical Equations – Example #3 n Algebraically solve 12/27/2021 Math 2 Honors

(C) Solving Radical Equations – Example #3 n Algebraically solve 12/27/2021 Math 2 Honors - Santowski 10

(C) Solving Radical Equations – Example #3 n And the algebraic solution n Explain

(C) Solving Radical Equations – Example #3 n And the algebraic solution n Explain what the term “extraneous solution” means Explain WHY they occur. n 12/27/2021 Math 2 Honors - Santowski 11

(D) Solving Radical Equations – Example #4 n Graphically solve n Algebraically solve 12/27/2021

(D) Solving Radical Equations – Example #4 n Graphically solve n Algebraically solve 12/27/2021 Math 2 Honors - Santowski 12

(D) Solving Radical Equations – Example #4 n And the algebraic solution n Explain

(D) Solving Radical Equations – Example #4 n And the algebraic solution n Explain what the term “extraneous solution” means Explain WHY they occur. n 12/27/2021 Math 2 Honors - Santowski 13

(E) Radical Equations – Predicting Extraneous Solutions n Solve and verify (algebraically) n Q?

(E) Radical Equations – Predicting Extraneous Solutions n Solve and verify (algebraically) n Q? In what domain do you expect the solution to be? ? ? 12/27/2021 Math 2 Honors - Santowski 14

(E) Radical Equations – Predicting Extraneous Solutions n Solve and verify (algebraically) 12/27/2021 Math

(E) Radical Equations – Predicting Extraneous Solutions n Solve and verify (algebraically) 12/27/2021 Math 2 Honors - Santowski 15

(E) Radical Equations – Predicting Extraneous Solutions n Let’s graphically solve 12/27/2021 Math 2

(E) Radical Equations – Predicting Extraneous Solutions n Let’s graphically solve 12/27/2021 Math 2 Honors - Santowski 16

(E) Radical Equations – Predicting Extraneous Solutions n Looking CAREFULLY at our graphic solution

(E) Radical Equations – Predicting Extraneous Solutions n Looking CAREFULLY at our graphic solution Is there not another logical way to eliminate the “extraneous” solution ? ? ? 12/27/2021 Math 2 Honors - Santowski 17

(E) Radical Equations – Predicting Extraneous Solutions n n n HINT: Range of this

(E) Radical Equations – Predicting Extraneous Solutions n n n HINT: Range of this radical function is y>0 Which should imply that f(x) = x+1 should be considered for only output values of y >0 So when is x + 1 > 0 for x > -1 n So our considerations for solutions should take into account x > -1 as well as x > -7 n Recall that the algebra gave us x = -3 and x = 2 so it should be obvious that x = -3 is an extraneous solution 12/27/2021 Math 2 Honors - Santowski 18

(F) Further Examples n Solve and verify without a calculator: n Are the following

(F) Further Examples n Solve and verify without a calculator: n Are the following statements (a) always true, (b) sometimes true or (c) never true 12/27/2021 Math 2 Honors - Santowski 19

(F) Further Examples n Solve algebraically and verify 12/27/2021 Math 2 Honors - Santowski

(F) Further Examples n Solve algebraically and verify 12/27/2021 Math 2 Honors - Santowski 20

Homework n p. 542 # 13 -23 odds, 24, 39, 41, 43, 57, 61

Homework n p. 542 # 13 -23 odds, 24, 39, 41, 43, 57, 61 -63 12/27/2021 Math 2 Honors - Santowski 21

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