Pre-Calculus Section 1.5 Equations Objectives: To solve quadratics by factoring, completing the square, and using the quadratic formula. To use the discriminant.

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Presentation transcript:

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.

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.

Ex 1. Solve by factoring. a)b)

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

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

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

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

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.

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

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

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

HW #5 p eoo, 69,70, 95, 96, 98, 99,100