Solving Quadratic Functions by Factoring. Factoring Review.

Slides:

Advertisements

Similar presentations

7-5 solving quadratic equations

Advertisements

Essential Question: What are the zeroes of a function?

Solving Quadratic Equations Tammy Wallace Varina High.

10-3: Solving Quadratic Equations

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

2-3 solving quadratic equations by graphing and factoring

1. Determine if f(x) has a minimum or maximum 2. Find the y-intercept of f(x) 3. Find the equation of the axis of symmetry of f(x) 4. Find the vertex of.

Quadratic Equations, Functions, and Models

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

7 January 2011 Algebra 2. Solving Quadratics by Graphing 1/7 Using a Graph To solve a quadratic equation with a graph, look for the points where the graph.

Solving Quadratic Equations

MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations.

Algebra II Honors POD Homework: p odds, odds (you must use completing the square), and 77, 83 Find all real solutions for the following:

Quadratic Relations Solving Quadratic Equations Day 2: Solve by Isolating the Variable Saturday, June 04, 20161Day 2 - Solve by Isolating the Variable.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

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.

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.

THE SLIDES ARE TIMED! KEEP WORKING! YOUR WORK IS YOUR OWN! Quadratic Systems Activity You completed one in class… complete two more for homework.

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.

BM 9: Solving Quadratic Equations. What is on the benchmark tomorrow?

An equation in the form … … can be solved using two methods discussed previously. Solving Equations Containing Trinomials 1.Factoring Method 2.Graphing.

Roots, Zeroes, and Solutions For Quadratics Day 2.

5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.

4.5 Quadratic Equations Wherever the graph of a function f(x) intersects the x-axis, f(x) = 0. A value of x for which f(x) = 0 is a zero of the function.

Do Now 1) Factor. 3a2 – 26a + 35.

MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations.

11-2 Solving Quadratic Equations By Graphing

Section 5-4(e) Solving quadratic equations by factoring and graphing.

SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.

Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.

Warm-Up: Solve each equation. Essential Question  How do I use the quadratic formula?

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

2.1 – Linear and Quadratic Equations Linear Equations.

6-2 Solving Quadratic Equations by Graphing Objectives: Students will be able to 1)Solve quadratic equations by graphing 2)Estimate solutions of quadratic.

Review: 6.5e Mini-Quiz 1. Solve: 16x 2 – 24x = – 4x Solve: (x – 3)(x – 2) = 30.

6.4 Completing the Square The Square Root Property.

Quadratic Formula. Solve x 2 + 3x – 4 = 0 This quadratic happens to factor: x 2 + 3x – 4 = (x + 4)(x – 1) = 0 This quadratic happens to factor: x 2.

Section )by graphing (using the calculator to identify the roots (x-intercepts)) 2)by factoring 3)by “completing the square” 4)by Quadratic Formula:

Goal: Solve quadratic equation by factoring the trinomial. Eligible Content: A

Algebra 1 EOC Summer School Lesson 13: Solve Quadratic Equations.

10.6 solving quadratic equations by factoring Solve x 2 + 2x – 3 using the quadratic formula X = 1 & -3 Now, factor the same equation (x + 3)(x – 1) Set.

Notes Over 9.4 Checking a Solution Using a Graph The solution, or roots of an equation are the x-intercepts. Solve the equation algebraically. Check the.

Quadratic Equations. Solving ax 2 + bx + c = 0 Taking Square Roots of Both Sides Graphing Factoring Completing the Square Quadratic Formula.

SAT Problem of the Day. 5.5 The Quadratic Formula 5.5 The Quadratic Formula Objectives: Use the quadratic formula to find real roots of quadratic equations.

Notes Over 10.4 Zero-Product Property if the product of two factors is zero, then at least one of the factors must be zero.

Warm-Up 1. Find the -Vertex -Y-Intercept -X-intercepts 2. Graph 3. Factor.

Skill Check Factor each polynomial completely.. 5-1: Solving Quadratic Equations by Factoring By Mr. Smith.

Notes P.5 – Solving Equations. I. Graphically: Ex.- Solve graphically, using two different methods. Solution – See graphing Calculator Overhead.

Solving Quadratic Equations by Graphing Chapter 9.2.

Find the number of real solutions for x2 +8x

Tuesday You need: - Calculator - Whiteboard, marker, eraser.

6.2 Solving Quadratic Equations by Graphing

A quadratic equation is written in the Standard Form,

9.3 Solving Quadratic Equations

Solving Quadratic Equations by Factoring

Equations with Variables on Both Sides Day 2

Objectives Solve quadratic equations by graphing or factoring.

Solving Quadratic Equations by Factoring

Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9 3

Using Factoring To Solve

Quadratics Lesson 2 Objective: Vertex Form of a Quadratic.

Solve Quadratics by Graphing ax2 +bx + c

Solving Quadratic Equations by Factoring

L5-7 Objective: Students will be able to solve quadratics by using the quadratic formula.

3.4 Solve by Factoring (Part 2)

Presentation transcript:

Solving Quadratic Functions by Factoring

Factoring Review

Vertex Form vs Standard Form

Value of the input variable (x) that makes the output variable (y=f(x)) equal zero. The x-intercepts The solution to the problem f(x) = 0 Also called the roots of the equation Zero of a Function

Zero Product Property

1. Write equation in standard form = 0 2. Factor 3.Set each factor = 0 (baby problems) 4. Solve each baby problem for x Solving by Factoring

1. Write equation in standard form = 0 2. Factor 3.Set each factor = 0 (baby problems) 4. Solve each baby problem for x Solving by Factoring

Graphing Solution vs Factoring Solution

1. Write equation in standard form = 0 2. Factor 3.Set each factor = 0 (baby problems) 4. Solve each baby problem for x Solving by Factoring

Graphing Solution vs Factoring Solution

1. Write equation in standard form = 0 2. Factor 3.Set each factor = 0 (baby problems) 4. Solve each baby problem for x Solving by Factoring

Graphing Solution vs Factoring Solution

Solve by Factoring

pp 82-83: (graph on calculator) 21-32, 34, 36, 61 Homework (HA2)

p 82: 1-27 (odd) Homework (Alg2)