Lesson 30 Solving Radical Equations Math 2 Honors

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Lesson 30 – Solving Radical Equations Math 2 Honors - Santowski 1

Lesson 30 – Solving Radical Equations Math 2 Honors - Santowski 1

Opening Investigation n We will investigate the idea of “equivalent systems” n Use a

Opening Investigation 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 Math 2 Honors - Santowski 2

Opening Investigation n We will investigate the idea of “equivalent systems” n Use a

Opening Investigation 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? Math 2 Honors - Santowski 3

Opening Investigation n We will investigate the idea of “equivalent systems” n Use a

Opening Investigation 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? Math 2 Honors - Santowski 4

(A) Solving Radical Equations n We can prepare graphic and algebraic solutions to radical

(A) Solving Radical Equations n We can prepare graphic and algebraic solutions to radical equations n As part of our algebraic solutions, we create “equivalent” systems, which we must justify n So our root functions have domain restrictions, we should state our restrictions at the beginning of our solutions Math 2 Honors - Santowski 5

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for ? ? ? ) n Math 2 Honors - Santowski 6

(A) Solving Radical Equations Examples n Graphic solution is: n Equivalent system: n Algebra

(A) Solving Radical Equations Examples n Graphic solution is: n Equivalent system: n Algebra solution is: Math 2 Honors - Santowski 7

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for ? ? ? ) n Math 2 Honors - Santowski 8

(A) Solving Radical Equations Examples n And the algebraic solution n Explain what the

(A) Solving Radical Equations Examples n And the algebraic solution n Explain what the term “extraneous solution” means Explain WHY they occur. n Math 2 Honors - Santowski 9

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for ? ? ? ) n Math 2 Honors - Santowski 10

(A) Solving Radical Equations Examples n And the algebraic solution n Explain what the

(A) Solving Radical Equations Examples n And the algebraic solution n Explain what the term “extraneous solution” means Explain WHY they occur. n Math 2 Honors - Santowski 11

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for

(A) Solving Radical Equations Examples n Graphically solve n Algebraically solve n (domain for ? ? ? ) n Math 2 Honors - Santowski 12

(A) Solving Radical Equations Examples n And the algebraic solution n Explain what the

(A) Solving Radical Equations Examples n And the algebraic solution n Explain what the term “extraneous solution” means Explain WHY they occur. n Math 2 Honors - Santowski 13

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

(B) Further Examples n Solve and verify without a calculator: n Are the following statements (a) always true, (b) sometimes true or (c) never true Math 2 Honors - Santowski 14

(B) Further Examples n Solve algebraically and verify Math 2 Honors - Santowski 15

(B) Further Examples n Solve algebraically and verify Math 2 Honors - Santowski 15

(B) Further Examples n If value of then determine the Math 2 Honors -

(B) Further Examples n If value of then determine the Math 2 Honors - Santowski 16

Working With Radicals – Intro to Conic Sections n n n (a) What is

Working With Radicals – Intro to Conic Sections n n n (a) What is the distance between any two given points on the Cartesian plane? (b) Determine the equation of the set of points that are an equidistance of 5 units from a fixed point of A(1, 2) (c) Determine the equation of a set of points that are equidistant from the line x = 5 and the point (9, 2) Math 2 Honors - Santowski 17

Working With Radicals – Intro to Conic Sections Math 2 Honors - Santowski 18

Working With Radicals – Intro to Conic Sections Math 2 Honors - Santowski 18

(C) Ellipses as Loci - Algebra n Since we are dealing with distances, we

(C) Ellipses as Loci - Algebra n Since we are dealing with distances, we set up our equation using the general point P(x, y), F 1 at (-3, 0) and F 2 at (3, 0) and the algebra follows on the next slide |PF 1| + |PF 2| = 10 19

(C) Algebraic Work 20

(C) Algebraic Work 20

(D) Graph of the Ellipse 21

(D) Graph of the Ellipse 21

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 Math 2 Honors - Santowski 22