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

2. 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

3. 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

4. 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

5. (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

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

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

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

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

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

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

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

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

14. 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

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

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

17. 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

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

19. (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

20. (C) Algebraic Work

21. (D) Graph of the Ellipse

22. Math 2 Honors - Santowski
Homework
p. 542 # odds, 24, 39, 41, 43, 53, 57, 61-63
Math 2 Honors - Santowski