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MTH 095 Intermediate Algebra Chapter 10 Complex Numbers and Quadratic Equations Section 10.3 Quadratic Equations: The Quadratic Formula Copyright © 2011 by Ron Wallace, all rights reserved.

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The Quadratic Formula Solve the following by completing the square …

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The Quadratic Formula If … … then … Yes! You MUST memorize and be able to use this formula.

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The Quadratic Formula If … … then … b 2 – 4ac is called the discriminant: less than zero two complex solutions i.e. they involve i equal to zero one real solution greater than zero two real solutions

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The Quadratic Formula Example (1 of 5)

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The Quadratic Formula Example (2 of 5)

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The Quadratic Formula Example (3 of 5)

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The Quadratic Formula Example (4 of 5)

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The Quadratic Formula Example (5 of 5)

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Methods for Solving Quadratic Equations Graphing Graph: f(x) = ax 2 + bx + c Solutions are the x-intercepts Factoring (mx + n)(rx + s) = 0 x = –n/m & –s/r Completing the Square Quadratic Formula NOTE: Assume the equation is in standard form: ax 2 + bx + c = 0

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