2-2: Solving Quadratic Equations Algebraically Learning Goals: Solve by factoring Solve by taking square root of both sides Solve by completing the square Solve by using quadratic formula © 2007 Roy L. Gover (www.mrgover.com)

Definition A quadratic, or second degree equation is one that can be written in the form for real constants a,b, and c with a≠0. This is the standard form for a quadratic equation.

Important Idea There are 4 techniques to algebraically solve quadratic equations: Factoring Taking square root of both sides Completing the square Using quadratic formula

Example Solve by factoring:

Definition The zero product property: If the product of real numbers is zero, then one or both of the numbers must be zero

Example What is wrong with this: Solve by factoring:

Try This Solve by factoring: Can you think of a way to check your answer?

Try This Solve by factoring: Hint: write in standard form

Example Solve by taking the square root of both sides: a. b.

Try This Solve by taking the square root of both sides:

Try This Solve by taking the square root of both sides. Give exact and approximate solutions.

Example What is wrong with this? Solve by taking the square root of both sides:

Example Complete the square for: 1. Half the coefficient of x: 1/2 of 12=6 2. Square this number and add to the expression

Important Idea Completing the square is the process of finding the number that will make the expression a perfect square trinomial.

Important Idea is a perfect square trinomial because it factors as:

Try This Complete the square for: then factor your result

Example Complete the square for: then factor your result. Use fractions only.

Example Solve by completing the square: 1. Move the constant to the right:

Example Solve by completing the square: 2. Complete the square and add to the left and right:

Example Solve by completing the square: 3. Factor left side and solve:

Try This Solve by completing the square:

Example Solve by completing the square… Before you complete the square, the coefficient of the squared term must be 1

Try This Solve by completing the square…fractions only.

Definition The solutions to are: These solutions are called the Quadratic Formula

Important Idea is called the discriminant 1. If there are 2 real solutions

Important Idea is called the discriminant 2. If there is 1 real solution

Important Idea is called the discriminant 3. If there are no real solutions

Example Solve using the quadratic formula. Leave answer in simplified radical form.

Try This Solve using the quadratic formula. Leave answer in simplified radical form.

Example Solve using the quadratic formula. Leave answer in simplified radical form.

Lesson Close State the quadratic formula from memory.

Practice 1. 95/1-23 odd (slides 1-12) 2. 95/26-34 even (slides 13-32)