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1.3 Quadratic Equations College Algebra: Equations and Inequalities

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Quadratic Equations Quadratic equation: is an equation of the form: ax 2 + bx + c =0 Forms of the Quadratic Equation: – Standard Form: – Zero Form: – Vertex Form:

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Zero-Factor Theorem If (x – r)(x –s) = 0 Then (x – r) = 0 (x – s) = 0 Where r and s are roots Solutions to equation are:

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Zero-Factor Theorem – Example Solve the equation

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Square Root Property If c > 0, the equation x 2 = c has two real roots:

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Completing the Square This is another method used to solve quadratic equations The goal is to convert the standard form into the Vertex form This creates a perfect square trinomial

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Completing the Square When a = 1 1. Group x terms on one side of the equation 2. Half the coefficient of x and then square it 3. Add the number found in 2 to both sides 4. Factor the perfect square trinomial and combine right side 5. Solve using the square root property

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Completing the Square When a > 1 1. Group x terms on one side of the equation Divide both side by a 2. Half the coefficient of x and then square it 3. Add the number found in 2 to both sides 4. Factor the perfect square trinomial and combine right side 5. Solve using the square root property

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The Quadratic Formula Solutions to ax 2 + bx + c =0

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The Quadratic Formula – Example Solve a=5, b =-9, c=-2

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The Discriminant The discriminant tells the nature of the roots of the quadratic equation

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The Discriminant – Examples

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Summary Quadratic Equations Zero-Factor Theorem Square Root Property Completing the Square The Quadratic Formula The DiscriminantDiscriminant

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