Solving Quadratic Equations Objective SWBAT solve quadratic equations

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Solving Quadratic Equations Objective: SWBAT solve quadratic equations and systems, and determine roots of

Solving Quadratic Equations Objective: SWBAT solve quadratic equations and systems, and determine roots of a higher order polynomial

Warm Up Factor the polynomial. 1. x 2 – 49 2. x 2 +

Warm Up Factor the polynomial. 1. x 2 – 49 2. x 2 + 6 x + 5 3. 3 x 2 +10 x – 8 4. 3 x 2 -24 5. 8 x 2 + 38 x -10

Quadratic Equations A Quadratic Equation is written in the form: ax 2 + bx

Quadratic Equations A Quadratic Equation is written in the form: ax 2 + bx + c = 0 where a ≠ 0, and a, b, c represent real numbers. • This form is called standard form • “Second degree equation”

Methods Used to Solve Quadratic Equations 1. Graphing 2. Factoring 3. Square Root Property

Methods Used to Solve Quadratic Equations 1. Graphing 2. Factoring 3. Square Root Property 4. Completing the Square 5. Quadratic Formula

Why so many methods? - Some methods will not work for all equations. -

Why so many methods? - Some methods will not work for all equations. - Some equations are much easier to solve using a particular method. - Variety is the spice of life.

Graphing � Graphing to solve quadratic equations does not always produce an accurate result.

Graphing � Graphing to solve quadratic equations does not always produce an accurate result. � If the solutions to the quadratic equation are irrational or complex, there is no way to tell what the exact solutions are by looking at a graph. � Graphing is very useful when solving contextual problems involving quadratic equations. � We are NOT going to focus on graphing in this course because of these reasons

Factoring � Factoring is typically one of the easiest and quickest ways to solve

Factoring � Factoring is typically one of the easiest and quickest ways to solve quadratic equations; HOWEVER… not all quadratic polynomials can be factored! � This means that factoring will not work to solve many quadratic equations.

Factor: 2 1. x – 24 = 0 (x + 4)(x – 6) =

Factor: 2 1. x – 24 = 0 (x + 4)(x – 6) = 0 x+4=0 x– 6=0 x=– 4 x=6

You Try �

You Try �

Square Root Property � This method is also relatively quick and easy; HOWEVER… it

Square Root Property � This method is also relatively quick and easy; HOWEVER… it only works for equations in which the quadratic polynomial is written in the following form: 2 2 x = n or (x + c) = n

Square Root Property Example: 2 1. x = 49 x=± 7

Square Root Property Example: 2 1. x = 49 x=± 7

Square Root Property Example: 2 2. (x + 3) = 25 x+3=± 5 x+3=5

Square Root Property Example: 2 2. (x + 3) = 25 x+3=± 5 x+3=5 x=2 x + 3 = – 5 x = – 8

Homework Day 1 �Textbook Pages 440 -441 ◦ # 29, 30, 31, 33, 37,

Homework Day 1 �Textbook Pages 440 -441 ◦ # 29, 30, 31, 33, 37, 39, 46