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SOLVING QUADRATIC EQUATIONS Factoring Method
Warm Up Factor the following. 1. x 2 – 4x – 45 2. x 2 + 2x – 48 3. 2x 2 -28x + 48
Zero – Product Property If A and B are expressions and AB = 0, then A = 0 or B = 0. (If the product of two expressions is zero, then on or both of the expressions equal zero.)
Example #1 Solve the following by factoring x 2 – 2x – 3 = 0
Example #2 Solve the following by factoring 3x 2 – 5x = 2
Quadratic Solutions In Quadratic Functions *x-intercepts *solutions *zeros of the function Are all looking for the same thing– what value of x will give you a y = 0
Example #3 Find the zeros of f(x) = x 2 – 8x
Example #4 Find the zeros of f(x) = 4x 2 + 28x + 49
Try These Solve the following by factoring 1. x 2 + 5x + 6 = 0 2. -4x 2 + 6x – 16 = 5x2 Find the zeros of the following functions. 1. f(x) = 3x 2 – 8x – 16 2. f(x) = x 2 – 7x + 12
Solving Quadratic Equations Using the Zero Product Property
Solving Quadratic Equations Algebraically Lesson 2.2.
Quadratic Equations, Functions, and Models
5.3.2 – Quadratic Equations, Finding Zeroes. Recall, we went over how to factor quadratics that are trinomials Example. Factor the expression x 2 + 7x.
Do Now: Factor x2 – 196 4x2 + 38x x2 – 36 (x + 14)(x – 14)
Solving Quadratic Equations
DO NOW: FACTOR EACH EXPRESSION COMPLETELY 1) 1) 2) 3)
Review of Radicals and Quadratic Equations Lesson 9.1.
1) What does x have to be for 3x = 0? 1) What does x have to be for 3(x -2) = 0 2) What does x have to be for (x–2) (x+3) = 0.
Example: 3x 2 + 9x + 6. Solving Quadratic Equations.
Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros.
Factor. 1)x² + 8x )y² – 4y – 21. Zero Product Property If two numbers multiply to zero, then either one or both numbers has to equal zero. If a.
Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics.
The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?
Solving Quadratic Equations by Graphing!. Quadratic functions vs. Quadratic equations Quadratic fxns are written in the following form f(x) = ax² + bx.
10-3 Solving Quadratic Equations. Quadratic Function (y = ax 2 +bx+c) Quadratic Equation ( ax 2 +bx+c=0)
6-2 Solving Quadratic Equations by Graphing
To add fractions, you need a common denominator. Remember!
Get out your notebooks! You will be able to solve quadratic equations by graphing. You will be able to estimate solutions of quadratic equations by graphing.
An equation in the form … … can be solved using two methods discussed previously. Solving Equations Containing Trinomials 1.Factoring Method 2.Graphing.
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