MTH 095 Intermediate Algebra Chapter 10 Complex Numbers and Quadratic Equations Section 10.3 Quadratic Equations: The Quadratic Formula Copyright © 2011.

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Presentation transcript:

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.

The Quadratic Formula Solve the following by completing the square …

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

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

The Quadratic Formula Example (1 of 5)

The Quadratic Formula Example (2 of 5)

The Quadratic Formula Example (3 of 5)

The Quadratic Formula Example (4 of 5)

The Quadratic Formula Example (5 of 5)

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