Section 2.5 – Quadratic Equations

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Presentation transcript:

Section 2.5 – Quadratic Equations

Quadratics Solving Quadratics Factoring Square Root Method A quadratic equation is an equation that can be written in the form where a, b, and c are real numbers and Examples: Solving Quadratics Factoring Square Root Method Completing the Square Quadratic Formula

Solve by Factoring Zero Product Principle: If , then a = 0 or b = 0.

Square Root Method If then .

Solve by Completing the Square 1 – Leading coefficient must be 1. Divide thorough by leading coefficient. 2 – Move constant to the right side. 3 – Find . Add to both sides. 4 – Factor on the left, simplify on the right. 5 – Take the Square Root of both sides. 6 – Simplify square roots = Right side simplifies with . 7 – Solve for the variable.

Solve by Completing the Square Side work:

Quadratic Formula

Quadratic Formula Ex.

The Discriminant The discriminant is the expression under the radical in the quadratic formula. Two imaginary solutions – complex conjugates One real solution Two distinct real solutions

The Discriminant Ex. Since the discriminant is negative, we will have two complex solutions that are complex conjugates. This means that the graph has NO x-intercepts.