Lesson 30 – Solving Radical Equations Math 2 Honors - Santowski Math 2 Honors - Santowski
Opening Investigation We will investigate the idea of “equivalent systems” Use a graph to solve the equation Explain what is meant by “equivalent systems” given your 2 solutions to the 2 equations Math 2 Honors - Santowski
Opening Investigation We will investigate the idea of “equivalent systems” Use a graph to solve the equation Is this an example of “equivalent systems” given your 2 solutions to the 2 equations? Math 2 Honors - Santowski
Opening Investigation We will investigate the idea of “equivalent systems” Use a graph to solve the equation Is this an example of “equivalent systems” given your 2 solutions to the 2 equations? Math 2 Honors - Santowski
(A) Solving Radical Equations We can prepare graphic and algebraic solutions to radical equations As part of our algebraic solutions, we create “equivalent” systems, which we must justify So our root functions have domain restrictions, we should state our restrictions at the beginning of our solutions Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples Graphically solve Algebraically solve (domain for ???) Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples Graphic solution is: Equivalent system: Algebra solution is: Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples Graphically solve Algebraically solve (domain for ???) Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples And the algebraic solution Explain what the term “extraneous solution” means Explain WHY they occur. Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples Graphically solve Algebraically solve (domain for ???) Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples And the algebraic solution Explain what the term “extraneous solution” means Explain WHY they occur. Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples Graphically solve Algebraically solve (domain for ???) Math 2 Honors - Santowski
(A) Solving Radical Equations - Examples And the algebraic solution Explain what the term “extraneous solution” means Explain WHY they occur. Math 2 Honors - Santowski
Math 2 Honors - Santowski (B) Further Examples Solve and verify without a calculator: Are the following statements (a) always true, (b) sometimes true or (c) never true Math 2 Honors - Santowski
Math 2 Honors - Santowski (B) Further Examples Solve algebraically and verify Math 2 Honors - Santowski
Math 2 Honors - Santowski (B) Further Examples If then determine the value of Math 2 Honors - Santowski
Working With Radicals – Intro to Conic Sections (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
Working With Radicals – Intro to Conic Sections Math 2 Honors - Santowski
(C) Ellipses as Loci - Algebra Since we are dealing with distances, we set up our equation using the general point P(x,y), F1 at (-3,0) and F2 at (3,0) and the algebra follows on the next slide |PF1| + |PF2| = 10
(C) Algebraic Work
(D) Graph of the Ellipse
Math 2 Honors - Santowski Homework p. 542 # 13-23 odds, 24, 39, 41, 43, 53, 57, 61-63 Math 2 Honors - Santowski