1. Solving Equations using Quadratic Techniques
Algebra II Mr. Gilbert
Chapter 7.3
Solving Equations using Quadratic Techniques
Standard & Honors
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2. Agenda
Warm up
Home Work
Lesson
Practice
Homework
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3. Homework Review
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4. Communicate Effectively
Quadratic Form : au2+bu+c
| a0 and a, b and c are Real, and
u is an expression in x
Recall:
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5. Example 1 Write an Expression in Quadratic Form (3)
Example 2 Solve Polynomial Equations (7)
Example 3 Solve Equations with Rational Exponents (4)
Example 4 Solve Radical Equations (3)
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Lesson 3 Contents

6. Write in quadratic form, if possible.
Answer:
Write in quadratic form, if possible.
Answer:
Write in quadratic form, if possible.
Answer: This cannot be written in quadratic form since
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Example 3-1a

7. Write in quadratic form, if possible.
Answer:
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Example 3-1d

8. Write each expression in quadratic form, if possible. a. b. c.
Answer:
Answer:
Answer: This cannot be written in quadratic form since
Answer:
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Example 3-1e

9. Write the expression on the left in quadratic form.
Solve .
Original equation
Write the expression on the left in quadratic form.
Factor the trinomial.
Factor each difference of squares.
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Example 3-2a

10. Use the Zero Product Property.or
Answer: The solutions are –5, –2, 2, and 5.
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Example 3-2b

11. Check. The graph of. shows
Check The graph of shows that the graph intersects the x-axis at –5, –2, 2, and 5.
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Example 3-2c

12. This is the sum of two cubes.
Solve .
Original equation
This is the sum of two cubes.
Sum of two cubes formula with a = x and b = 6 or
Zero Product Property
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Example 3-2d

13. Replace a with 1, b with –6, and c with 36.
The solution of the first equation is –6. The second equation can be solved by using the Quadratic Formula.
Quadratic Formula
Replace a with 1, b with –6, and c with 36.
Simplify.
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Example 3-2e

14. Answer: The solutions of the original equation are
Simplify.
Answer: The solutions of the original equation are
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Example 3-2f

15. Solve each equation. a. b. Answer: –3, –1, 1, 3 Answer: 1/17/2019
Example 3-2g

16. Write the expression on the left in quadratic form.
Solve
Original equation
Write the expression on the left in quadratic form.
Factor the trinomial.
Zero Product Property or
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Example 3-3a

17. Isolate x on one side of the equation. or
Raise each side to the fourth power.
Simplify.
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Example 3-3b

18. Check Substitute each value into the original equation.
Answer: The solution is 81.
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Example 3-3c

19. Solve
Answer: –8, –27
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Example 3-3d

20. Rewrite so that one side is zero.
Solve
Original equation
Rewrite so that one side is zero.
Write the expression on the left side in quadratic form.
Factor.
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Example 3-4a

21. Zero Product Property or Solve each equation.
Answer: Since the square root of x cannot be negative, the equation has no solution. Thus, the only solution of the original equation is 9.
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Example 3-4b

22. Solve
Answer: 25
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Example 3-4c

23. Homework
See Syllabus 7.3
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