Solving Equations using Quadratic Techniques Algebra II Mr. Gilbert Chapter 7.3 Solving Equations using Quadratic Techniques Standard & Honors 1/17/2019

Agenda Warm up Home Work Lesson Practice Homework 1/17/2019

Homework Review 1/17/2019

Communicate Effectively Quadratic Form : au2+bu+c | a0 and a, b and c are Real, and u is an expression in x Recall: 1/17/2019

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) 1/17/2019 Lesson 3 Contents

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 1/17/2019 Example 3-1a

Write in quadratic form, if possible. Answer: 1/17/2019 Example 3-1d

Write each expression in quadratic form, if possible. a. b. c. Answer: Answer: Answer: This cannot be written in quadratic form since Answer: 1/17/2019 Example 3-1e

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. 1/17/2019 Example 3-2a

Use the Zero Product Property. or Answer: The solutions are –5, –2, 2, and 5. 1/17/2019 Example 3-2b

Check. The graph of. shows Check The graph of shows that the graph intersects the x-axis at –5, –2, 2, and 5. 1/17/2019 Example 3-2c

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 1/17/2019 Example 3-2d

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. 1/17/2019 Example 3-2e

Answer: The solutions of the original equation are Simplify. Answer: The solutions of the original equation are 1/17/2019 Example 3-2f

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

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 1/17/2019 Example 3-3a

Isolate x on one side of the equation. or Raise each side to the fourth power. Simplify. 1/17/2019 Example 3-3b

Check Substitute each value into the original equation. Answer: The solution is 81. 1/17/2019 Example 3-3c

Solve Answer: –8, –27 1/17/2019 Example 3-3d

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. 1/17/2019 Example 3-4a

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. 1/17/2019 Example 3-4b

Solve Answer: 25 1/17/2019 Example 3-4c

Homework See Syllabus 7.3 1/17/2019