Sec. 1.4 Quadratic Equations.

Slides:



Advertisements
Similar presentations
10-6 Solving Quadratic Equations by Factoring
Advertisements

2.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.
Solving Quadratic Equations Algebraically Lesson 2.2.
Solving Equations by Factoring
9.4 – Solving Quadratic Equations By Completing The Square
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations Section 1.3
3.5 Quadratic Equations OBJ:To solve a quadratic equation by factoring.
Copyright © Cengage Learning. All rights reserved.
Quadratic Equations, Functions, and Models
Algebra 1 Jarrett Sutter
6.5 – Solving Equations with Quadratic Techniques.
OBJ: To solve a quadratic equation by factoring
DO NOW: FACTOR EACH EXPRESSION COMPLETELY 1) 1) 2) 3)
Solving Quadratic Equations by Factoring MATH 018 Combined Algebra S. Rook.
Factor: Factor: 1. s 2 r 2 – 4s 4 1. s 2 r 2 – 4s b b 3 c + 18b 2 c b b 3 c + 18b 2 c 2 3. xy + 3x – 2y xy + 3x – 2y -
Quadratics Solving equations Using “Completing the Square”
Pre-Calculus Section 1.5 Equations Objectives: To solve quadratics by factoring, completing the square, and using the quadratic formula. To use the discriminant.
Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics.
The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.
Solving Quadratic Equations Quadratic Equations: Think of other examples?
Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.
Solving Quadratic Equations. Factor: x² - 4x - 21 x² -21 a*c = -21 b = -4 x + = -21 = x 3x3x x 3 (GCF) x-7 (x – 7)(x + 3)
PreCalculus Section P.1 Solving Equations. Equations and Solutions of Equations An equation that is true for every real number in the domain of the variable.
Completing the Square SPI Solve quadratic equations and systems, and determine roots of a higher order polynomial.
Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.
PreCalculus Section 1.6 Solve quadratic equations by: a. Factoring b. Completing the square c. Quadratic formula d. Programmed calculator Any equation.
Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.
Lesson 6.5: The Quadratic Formula and the Discriminant, pg. 313 Goals: To solve quadratic equations by using the Quadratic Formula. To use the discriminant.
2.2 Solving Quadratic Equations Algebraically Quadratic Equation: Equation written in the form ax 2 + bx + c = 0 ( where a ≠ 0). Zero Product Property:
Solve Quadratic Functions by Completing the Square
PreCalculus Section 1. 6 Solve quadratic equations by: a. Factoring b
Solve Quadratic Equations by Completing the Square
Warm up Factor the expression.
Aim: What are the properties of a quadratic equation?
Chapter 4 Quadratic Equations
The Square Root Principle & Completing the Square
The Quadratic Formula..
Solving Equations by Factoring
10.4 Solving Factored Polynomial Equations
Objectives Solve quadratic equations by factoring.
Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
5.5 Completing the Square.
Solving Equations by Factoring
Section 11.2 The Quadratic Formula.
The Quadratic Formula.
1. Use the quadratic formula to find all real zeros of the second-degree polynomial
13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
9.3 Solve Quadratics by Completing the Square
9.4 Solving Quadratic Equations
1B.1- Solving Quadratics:
2.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
5.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
Review: Simplify.
Warm-Up: September 30 / October 1, 2015 Factor each expression
Standard Form Quadratic Equation
13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
Solving Quadratic Equations
13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
9.5 Factoring to Solve Quadratic Equations
Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.
Topic: The Parabola.
The Quadratic Formula..
The Quadratic Formula..
Solving Equations by Factoring
quadratic formula. If ax2 + bx + c = 0 then
Ch 10: Polynomials G) Completing the Square
Presentation transcript:

Sec. 1.4 Quadratic Equations

Quadratic Equation in general form ax2 + bx + c = 0 Also called a 2nd degree polynomial

Method in this section for solving Factoring Extracting square roots Completing the square Quadratic formula

Zero Factor Property If ab = 0 then a = 0 or b = 0

To use this Factor the left side of ax2 + bx + c = 0 Then set each linear factor equal to 0 and solve

Factoring Ex. 1 A) 2x2 + 9x + 7 = 3 B) 6x2 – 3x = 0

Extracting Square Roots For u2 = d when d > 0 u is an alg. expression

So for u2 = d U = ± √d

EX 2 A) 4x2 = 12 B) (x-3)2 = 7