Quadratic Formula & the Discriminant

Slides:



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

5.3 Complex Numbers; Quadratic Equations with a Negative Discriminant.
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
4.8 Quadratic Formula and Discriminant
Bell Ringer: Find the zeros of each function.
Solving Quadratic Equations by the Quadratic Formula
Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula. Discriminant.
Solving Quadratic Equations Using Completing the Square and the Quadratic Formula.
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.
Derivation of the Quadratic Formula The following shows how the method of Completing the Square can be used to derive the Quadratic Formula. Start with.
The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?
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.
CPM Section 9.4A Quadratic Formula. Thus far we have considered two methods for solving quadratic function- factoring and using the square root property.
4.2 Quadratic Functions Objective: Solve quadratic equations. Use the discriminant to describe the roots of a quadratic equation.
Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.
Notes Over 5.6 Quadratic Formula
4.8 “The Quadratic Formula” Steps: 1.Get the equation in the correct form. 2.Identify a, b, & c. 3.Plug numbers into the formula. 4.Solve, then simplify.
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.
9.2 THE DISCRIMINANT. The number (not including the radical sign) in the quadratic formula is called the, D, of the corresponding quadratic equation,.
MM2A4. Students will solve quadratic equations and inequalities in one variable. b. Find real and complex solutions of equations by factoring, taking square.
Algebra 2 Notes March 23, Do you remember the Quadratic Formula? - Work with the people around you. Brainstorm and try and remember the quadratic.
Evaluate
ANSWERS!. Completing the Square Level 1 Answers Completing the Square Level 2 Answers.
Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.
Factoring & Solving Quadratics Equations Intermediate Algebra Final Exam Review.
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.
3.4 Chapter 3 Quadratic Equations. x 2 = 49 Solve the following Quadratic equations: 2x 2 – 8 = 40.
Section 2.5 – Quadratic Equations
5.6 Quadratic Formula & Discriminant
How do I solve quadratic equations using Quadratic Formula?
Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –
4.6 Quadratic formula.
Lesson 5.6: The Quadratic Formula & the Discriminant
Solving Quadratic Equations by the Quadratic Formula
Solving Quadratic Equations by the Complete the Square Method
Solving Quadratic Equations by the Quadratic Formula
The QUADRATIC Discriminant.
4.6 Quadratic formula.
Solve x2 + 2x + 24 = 0 by completing the square.
Warmup 1. Solve x2 – 14x + 9 = 0 by completing the square.
Section 5.8 The Quadratic Formula
5.6 The Quadratic Formula and the Discriminant
4.8 The Quadratic Formula and the Discriminant
Unit 7 Day 4 the Quadratic Formula.
Skills Check ALL Factoring
4.8 Use the Quadratic Formula & the Discriminant
Questions over HW?.
Warm up – Solve by Completing the Square
The Quadratic Formula.
Section 5.8 The Quadratic Formula
Warm Up Solve: (x – 4)(2x – 1) = 0 2. Solve: x² – 9x = 36.
Review.
Review: Simplify.
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
Lessons The quadratic Formula and the discriminant
3.4 – The Quadratic Formula
Questions over HW?. Skills Check Radical Operations and Solving by Square Roots after HW Check.
Click to begin..
Using the Quadratic Formula to Solve Quadratic Equations
  Warm Up:.
Quadratic Formula & Discriminant
Solving Quadratic Equations by the Quadratic Formula
Presentation transcript:

Quadratic Formula & the Discriminant Chapter 4.8 Quadratic Formula & the Discriminant p296 22-30, 40, 41, 44 #29 Who solved the square root of infinity.

From last week

Discriminant The part of the quadratic equation under the radical is called the discriminant. The discriminant can be used to determine the number of solutions of a quadratic. Two Real Solutions One Real Solution Two Imaginary Solutions

Give the number & types of solutions for each. Examples Give the number & types of solutions for each. Two Real Solutions Two Imaginary Solutions

Quadratic Equation

Example a b c

Example a b c

Example a b c

extra

Some times you will not get a real number

Example a b c

You can also use the quadratic equation to Factor

Assignment p296 22-30, 40, 41, 44