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.

Slides:

Advertisements

Similar presentations

If b2 = a, then b is a square root of a.

Advertisements

Day 5 Simplify each expression: Solving Quadratic Equations I can solve quadratic equations by graphing. I can solve quadratic equations by using.

Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =

7.1 – Completing the Square

Solve Using Best Method

Solving Quadratic Equations by the Quadratic Formula

Using the Quadratic Formula to Solve a Quadratic Equation

Solving Quadratic Equations by the Quadratic Formula

Notes Over 9.7 Using the Discriminant The discriminant is the expression under the radical: If it is Positive: Then there are Two Solutions If it is Zero:

Using the factoring method, what are the solutions of y = x 2 + 5x + 6.

Solving Quadratic Equations

Solving Quadratic Equations by Factoring. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x².

CA STANDARDS 20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Agenda 1.) Lesson.

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

Solving Quadratics. Methods for Solving Quadratics Graphing Factoring Square Root Method Completing the Square Quadratic Formula.

Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.

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.

Discriminant Recall the quadratic formula: x = -b ±√ b2 - 4ac 2a.

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?

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.

Roots, Zeroes, and Solutions For Quadratics Day 2.

Solving Quadratic Equations using the Quadratic Formula

Warm-up 1.What are the different ways to solve quadratic equation? Solve the following problem by completing the square.

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

By: Adam Linnabery. The quadratic formula is –b+or-√b 2 -4ac 2a an example of how it is used: X 2 -4x-12=0 the coefficient of x 2 is 1 therefore the value.

Bell Work Solve the Equation by Factoring or using Square Roots: Solve the equation by using the quadratic formula: 3. Identify the parts of a parabola:

11-2 Solving Quadratic Equations By Graphing

Lecture 301 Solving Quadratic Equations Two Methods Unit 4 Lecture 30 Solving Quadratic Equations.

Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.

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.

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

x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.

ANSWERS!. Completing the Square Level 1 Answers Completing the Square Level 2 Answers.

Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D

Factoring & Solving Quadratics Equations Intermediate Algebra Final Exam Review.

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.

Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation It.

SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The.

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

10.6B Best Method. Standard Form: Square Root Method: 1. When b = 0 2. Get x 2 alone 3. Square root both sides 4. plus/minus answer.

Warm Ups Term 2 Week 6.

Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equations by the Complete the Square Method

Solving Using Quadratic Equations

5-Minute Check Lesson 4-2 Answer: 2

Solve x2 + 2x + 24 = 0 by completing the square.

9.3 Solving Quadratic Equations

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Skills Check ALL Factoring

The Discriminant Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.

Quadratic Formula & the Discriminant

Section 9.5 Day 1 Solving Quadratic Equations by using the Quadratic Formula Algebra 1.

Quadratic Equations.

5.6 Quadratic Formula & Discriminant

Solving Quadratic Equations by the Quadratic Formula

Skills Check Solve by Factoring and Square Roots

Questions over HW?. Skills Check Radical Operations and Solving by Square Roots after HW Check.

Algebra 9.6 The Discriminant.

Quadratic Formula & Discriminant

Solve using factoring or square root property.

Equations Involving Absolute Value

Presentation transcript:

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 + 3x – 4 = (x + 4)(x – 1) = 0 Solutions: x = -4, x = 1 Solutions: x = -4, x = 1 What would the process look like using the quadratic formula? What would the process look like using the quadratic formula?

Solve 2x 2 – 4x – 3 = 0. Note: The solution or roots or zeroes of a quadratic are usually required to be in the "exact" form of the answer. That means leave them in radical form! Note: The solution or roots or zeroes of a quadratic are usually required to be in the "exact" form of the answer. That means leave them in radical form!

Solve x(x – 2) = 4

Making Connections to the Graph You can tell how many x-intercepts you're going to have from the value inside the square root. You can tell how many x-intercepts you're going to have from the value inside the square root. Solve 9x x + 4 = 0 using the quadratic formula. Then graph the equation. Solve 9x x + 4 = 0 using the quadratic formula. Then graph the equation.

Solve 3x 2 + 4x + 2 = 0. What do your solutions look like? How does that change the graph? What do your solutions look like? How does that change the graph?