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2.2. Solving Quadratic Equations Algebraically. Objectives: Solve equations by: Factoring Square Root of Both Sides Completing the Square Quadratic Formula Solve equations in quadratic form. Definition of a Quadratic Equation. An equation that can be written in the form

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## Solving Quadratic Equations Algebraically

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**2.2**Solving Quadratic Equations Algebraically Objectives: Solve equations by: Factoring Square Root of Both Sides Completing the Square Quadratic Formula Solve equations in quadratic form.**Definition of a Quadratic Equation**An equation that can be written in the form ax2 + bx + c = 0 with real constants a, b, & c, with a ≠ 0. Techniques to solve a quadratic equation: • Techniques that sometimes work Factoring Taking the square root of both sides of an equation • Techniques that always work Completing the Square Using the Quadratic Formula**Example #1aSolving by Factoring**Solve by Factoring:**Example #1bSolving by Factoring**Solve by Bottoms Up Method: Don’t forget to first factor out the GCF, if necessary. To factor this trinomial you must first multiply a by c, factor normally, divide both factors by a & reduce, and finally bring “bottoms up”.**Example #2Solving ax2 = b**Solve by Taking the Square Root of Both Sides:**Example #3Solving a(x−h)2 = k**Solve by Taking the Square Root of Both Sides:**Example #4Solving a Quadratic Equation by Completing the**Square Solve by Completing the Square: Completing the square only works when the coefficient of x2 is a 1. Always divide every term by the leading coefficient before attempting to complete the square.**Example #4Solving a Quadratic Equation by Completing the**Square Solve by Completing the Square: Remember after completing the square, add it to both sides of the equation.**Example #5Solving a Quadratic Equation by Using the**Quadratic Formula Solve by Using the Quadratic Formula: Quadratic equations must be in Standard Form ax2 + bx + c = 0 before using the Quadratic Formula.**The Discriminant**The discriminant is used to determine the number of solutions without solving the problem.**Example #6Determining the Number of Solutions by Using the**Discriminant Find the Number of Solutions: −31 is NOT a solution to the equation. Since the discriminant is negative, this means that there is no real solution to the equation.**Example #7Polynomials in Quadratic Form**Solving an Equation in Quadratic Form: Compare this polynomial equation with the quadratic form: ax2+ bx + c = 0 This polynomial can be factored using Bottoms Up!

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