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Published byEvelyn Munoz Modified over 3 years ago

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Section 10-5 Factor to Solve Quadratic Equations SPI 23E: Find the solution to a quadratic equation given in standard form SPI 23F: select the solution to a quadratic equation given solutions represented in graphical form Objectives: Solve (find real number solutions) by factoring The solutions of a quadratic equation are: the x-intercepts since they are on the real number line a quadratic equation can have solutions as follows: Two Solutions (touches x-axis twice) One Solutions (touches x-axis once) No Solution (does not touch x-axis)

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Methods of Finding Real Number Solutions Two Methods for Solving Quadratic Equations: Factoring and using the Zero-Product Property Using the Quadratic Formula

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Zero-Product Property Factor x 2 + 7x + 10 = 0 Both conditions must be true Factors of the problem are (x + 2)(x + 5) Factors of 10Sum of Factors 1 1011 2 57 Solve (x + 2)(x + 5) = 0 x + 2 = 0 or x + 5 = 0 x + 2 – 2 = 0 – 2 or x + 5 – 5 = 0 – 5 x = - 2 or x = - 5 There are two real number solutions to the quadratic equation. To find the real number solutions, use the Zero-Product Property

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Solve x 2 + x – 42 = 0 by factoring. (x + 7)(x – 6) = 0Factor using x 2 + x – 42 x + 7 = 0orx – 6 = 0Use the Zero-Product Property. x = –7orx = 6 Solve for x. Factor to Solve a Quadratic Equation Both conditions must be true Factors of the problem are (x + 7)(x -6) Factors of - 42Sum of Factors 2 -21-19 -6 7-6 + 7 = 1

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Practice 3. Solve by factoring x 2 – 16 x + 55 = 0. 1. Use the zero property to solve (x – 3) (x – 7) = 0. 4. Solve by factoring m 2 – 5m – 14 = 0. 3 and 7 0 and 2.5 5 and 11 -2 and 7 2. Use the zero property to solve – 3n(2n – 5) = 0.

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