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

Slides:

Advertisements

Similar presentations

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

Advertisements

Complex Number A number consisting of a real and imaginary part. Usually written in the following form (where a and b are real numbers): Example: Solve.

4.8 Quadratic Formula and Discriminant

The Quadratic Formula..

Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equations by the Quadratic Formula

4.8: Quadratic Formula HW: worksheet

Sec 5.6 Quadratic Formula & Discriminant Quadratic Formula (Yes, it’s the one with the song!) If ax 2 + bx + c = 0 and a ≠ 0, then the solutions (roots)

Objectives: To solve quadratic equations using the Quadratic Formula. To determine the number of solutions by using the discriminant.

Warm up – Solve by Taking Roots. Solving by the Quadratic Formula.

Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula. Discriminant.

Quadratic Equations, Functions, and Models

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

Goals: To solve quadratic equations by using the Quadratic Formula.

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.

5.6 Quadratic Formula & Discriminant

Solving Quadratic Equations by the Quadratic Formula Section 4.8.

3.8 Warm Up Write the function in vertex form (by completing the square) and identify the vertex. a. y = x² + 14x + 11 b. y = 2x² + 4x – 5 c. y = x² -

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

4.8 Do Now: practice of 4.7 The area of a rectangle is 50. If the width is x and the length is x Solve for x by completing the square.

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.

5.6 Quadratic Formula & Discriminant By: L. Keali’i Alicea.

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

5.6 – Quadratic Equations and Complex Numbers Objectives: Classify and find all roots of a quadratic equation. Graph and perform operations on complex.

To add fractions, you need a common denominator. Remember!

More about Quadratic Equations November 16, 2009.

WARM UP WHAT TO EXPECT FOR THE REST OF THE YEAR 4 May The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June Adding.

Pre-Calculus Lesson 5: Solving Quadratic Equations Factoring, quadratic formula, and discriminant.

Quadratic Formula You can use this formula to find the solutions(roots) to a quadratic equation. This formula can be broken up into 2 parts: b 2 – 4ac.

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

10-4 Solving Quadratic Equations by Using the Quadratic Formula

4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation.

Solving Quadratic Formula using the discriminant.

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

Getting Started The objective is to be able to solve any quadratic equation by using the quadratic formula. Quadratic Equation - An equation in x that.

Notes Over 5.6 Quadratic Formula

Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

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:

Warm UP Take a few minutes and write 5 things you remember about the quadratic formula?? Take a few minutes and write 5 things you remember about the quadratic.

ALGEBRA 1 SECTION 10.7 Interpret the Discriminant Big Idea: Determine the number of solutions to a quadratic equation. Essential Question: How do you use.

Warm-Up Solve each equation by factoring. 1) x x + 36 = 02) 2x 2 + 5x = 12.

Warm Up  1.) Write 15x 2 + 6x = 14x in standard form. (ax 2 + bx + c = 0)  2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.

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.

9.4 Solving Quadratic Equations Standard Form: How do we solve this for x?

5-8 Quadratic Formula Hubarth Algebra II. Ex 1 Using the Quadratic Formula Solve x = –3x. x 2 + 3x + 2 = 0 x = –b ± b 2 – 4ac 2a x = –3 ± (3) 2.

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.

2.2 Solving Quadratic Equations Algebraically Quadratic Equation: Equation written in the form ax 2 + bx + c = 0 ( where a ≠ 0). Zero Product Property:

5.6 Quadratic Formula & Discriminant

The Quadratic Formula & Discriminant

Solving Quadratic Equations by the Quadratic Formula

The Quadratic Formula..

Solving Quadratic Equations by Graphing

Section 5.8 The Quadratic Formula

Unit 7 Day 4 the Quadratic Formula.

4.8 Use the Quadratic Formula & the Discriminant

Section 5.8 The Quadratic Formula

9-6 The Quadratic Formula and Discriminant

Warm Up Solve: (x – 4)(2x – 1) = 0 2. Solve: x² – 9x = 36.

5.6 Quadratic Formula & Discriminant

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

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

Section 4.7 – Quadratic Formula

Using the Quadratic Formula to Solve Quadratic Equations

Quadratic Formula & Discriminant

1.) What is the value of the discriminant?

Presentation transcript:

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

Review from yesterday... Solve: 1. 0 = x2 + 2x x2 + 2x + 1 = 0

Discriminant: b2 - 4ac * used to determine the number of solutions of a quadratic equation If the discriminant is: zero: 1 solution negative: no real solutions positive: 2 solutions (note...if it is a perfect square...it is factorable)

Find the value of the discriminant and tell how many solutions each quadratic equation will have. ex 1: -3x2 + 5x = 1

ex 3: x2 = -10x - 25 ex 2: x2 - 2x = -4

ex 4: Find the number of x-intercepts of the graph of the following quadratic equation: y = x2 + 6x + 3