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Pre-Calculus Section 1.5 Equations Objectives: To solve quadratics by factoring, completing the square, and using the quadratic formula. To use the discriminant to determine the number of real solutions to a quadratic. To solve absolute value equations.

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Quadratic Equations The values of the variables that make an equation true are called roots or solutions of the equation. A quadratic equation has the form ax 2 + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.

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Ex 1. Solve by factoring. a)b)

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Ex 2. Solve by completing the square. a)b)

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Quadratic Formula The roots of a quadratic equation ax 2 + bx + c = 0 where a ≠ 0 are

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Ex 3. Find all solutions of each equation. a) b)

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Class Work Find all real solutions. Use the indicated method to solve. 1. by factoring 2. by completing the square 3. by quadratic formula

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The Discriminant is called the discriminant of a quadratic equation. It tells us how many real solutions there are to a quadratic equation. If D > 0, then there are 2 real solutions. If D = 0, then there is 1 real solution. If D < 0, then there are no real solutions.

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Ex 4. Use the discriminant to determine how many real solutions of each equation. Do not solve the equation. a) b) c)

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Absolute Value Equations Ex 5. Find all real solutions. a) b)

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Class Work 4. Use the discriminant to determine the number of real solutions to the equation. 5. Find all real solutions.

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HW #5 p55 37-61 eoo, 69,70, 95, 96, 98, 99,100

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