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Chapter 10 Quadratic Equations and Functions Lesson 10-1a Solving Quadratic Equations by Factoring and using the Square Root Property

Objective: Students will solve quadratic equations by factoring and by using the square root property.

Solving Quadratic Equations by Factoring

Solve Then check the solutions. – 4y = 0 4y(3y – 1) = 0 3y – 1 = 0 or Answer: y = 0, 3 Example 2-5a

Solve = 0 = (2xy -2y) + (7x – 7) = 0 = 0 = 0 Answer: y = - 7 2 and x = 1 Example 2-2a

Solve by grouping. a = 15 and c = –8 therefore ac = –120 What 2 numbers multiply to make -120 and add to make –14? 6 and –20 Replace -14b with 6b – 20b Group 15b2 + 6b – 20b – 8 = 0 (15b2 + 6b) – 1(20b + 8) = 0 3b(5b + 2) – 4(5b + 2) = 0 6b –20b –14b TRUE

Now that the equation is factored, SOLVE IT. Answer: The solution set is b = Check your answers. Example 4-4a

The Square Root Property

The solutions are x = 3 and x = - 3 . Solve 4x2 = 12 by the Square Root Property. x2 = 3 𝑥 2 = 3 x = ± 3 The solutions are x = 3 and x = - 3 . Check these in the original equation.

Solve (3x + 5)2 – 16 = 0 by the Square Root Property. 𝑥=− 5 3 ± 4 3 The solutions are x = - 1 3 and x = -3. Check these in the original equation.

Lesson Summary: Objective: Students will solve quadratic equations by factoring and by using the square root property.

Preview of the next Lesson: Objective: Students will solve word problems by solving quadratic equations by factoring and using the square root property.

Homework 553+554/1,9,17...81

Stand Up Please