How many solutions does your quadratic have?. 43210 In addition to level 3, students make connections to other content areas and/or contextual situations.

Slides:

Advertisements

Similar presentations

Finding Complex Roots of Quadratics

Advertisements

Derive the Quadratic Formula In addition to level 3, students make connections to other content areas and/or contextual situations outside of math.

Quadratic Functions, Quadratic Expressions, Quadratic Equations

Graphs of Quadratic Functions In addition to level 3, students make connections to other content areas and/or contextual situations outside of.

Simplify Expressions in Exponential or Radical Form.

Graphing Quadratic Equations from the Vertex Form.

4.8 Quadratic Formula and Discriminant

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.

8.2 Negative and Zero Exponents I love exponents!.

Sketching quadratic functions To sketch a quadratic function we need to identify where possible: The y intercept (0, c) The roots by solving ax 2 + bx.

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.

Algebra 1B Chapter 9 Solving Quadratic Equations The Discriminant.

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

Objective - To use the discriminant to determine the number of real solutions for a quadratic. Quadratic FormulaDiscriminant Used to find the roots of.

5.6 Quadratic Formula & Discriminant

Solving Quadratic Equations by Finding Square Roots.

Solving quadratic equations by graphing. X Y I x² - 2x = 3 You have to rewrite the equation to find the vertex before you can graph this function Use.

Graphing Quadratics: putting it all together In addition to level 3, students make connections to other content areas and/or contextual situations.

Review How do we solve quadratic equations? 1.) Factoring using “Bottoms Up” 2.) if its not factorable by “Completing the Square”

X-Intercepts/Roots: Discriminant and the Quadratic Formula 1. Review: X-Intercepts are the Roots or Solutions x y Y = f(x) = 0 at the x-intercepts (curve.

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.

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

Graphs of Quadratic Equations In addition to level 3, students make connections to other content areas and/or contextual situations outside of.

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

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.

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.

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

$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400.

Solving Quadratic Formula using the discriminant.

Solving Quadratic Equations by Factoring In addition to level 3, students make connections to other content areas and/or contextual situations.

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.

Factoring Quadratic Trinomials In addition to level 3, students make connections to other content areas and/or contextual situations outside of.

Sample Problems for Class Review

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

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

Complex Numbers Quadratic Formula Completing The Square Discriminant.

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.

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

Solving the Quadratic Equation by Completing the Square.

Key Components for Graphing a Quadratic Function.

Chapter 9 Quadratic Equations And Functions By Chris Posey and Chris Bell.

Concept 25 Learning Target: I can solve quadratics by using the quadratic formula.

Created by Judy L. McDaniel. Be sure to write a quadratic equation in before using most methods for solving. (not necessarily for the Square Root Prop.)

Lesson 9.5 Objective: To solve quadratic equations using the quadratic formula. Quadratic formula: When Then the value of x is… What formula can be used.

How do I solve quadratic equations using Quadratic Formula?

The Quadratic Formula & Discriminant

Discriminant and Quadratic

Warm Up Use a calculator to evaluate

Chapter 4 Quadratic Equations

Quadratic Functions, Quadratic Expressions, Quadratic Equations

Solving quadratics methods

Find the number of real solutions for x2 +8x

The Discriminant.

Unit 7 Day 4 the Quadratic Formula.

Solving Quadratic Equations using the Quadratic Formula

9-6 The Quadratic Formula and Discriminant

MATH CP Algebra II Exploring Quadratic Functions and Inequalities

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

The Discriminant CA 22.0, 23.0.

Warm-Up 1 ( ) 1) x2 – 7x + 12 = 0 (by factoring)

Algebra 9.6 The Discriminant.

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

Warm Up Using the quadratic formula find the zeros of the following:

Factorise and solve the following:

Presentation transcript:

How many solutions does your quadratic have?

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will sketch graphs of quadratics using key features and solve quadratics using the quadratic formula. - Students will be able to write, interpret and graph quadratics in vertex form. Students will be able to use the quadratic formula to solve quadratics and are able to identify some key features of a graph of a quadratic. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 10 Learning Goal – (HS.A-REI.B.4, HS.F-IF.B.4, HS.F-IF.C.7, HS.F-IF.C.8) = Students will sketch graphs of quadratics using key features and solve quadratics using the quadratic formula.

Solve the following three quadratics using only the quadratic formula. Show your work. 1. x 2 – 2x + 1 = 02. 3x 2 + 4x + 8 = 03. 2x 2 + 7x - 4 = 0 Describe these three solutions. What do you notice about the formula while you were solving it that provided you with these answers?

The expression under the radical is called the discriminant : b 2 – 4ac  The value of the discriminant determines how many solutions the quadratic will have.  Equation 1: the discriminant was zero, there was only 1 solution.  Equation 2: the discriminant was a negative number, there was no solution.  Equation 3: the discriminant was a positive number, there were two solutions.  Remember: when we solve a quadratic, we are finding where the parabola intercepts the x-axis.

 What is the difference between these three graphs?  Which of these three graphs belongs to a quadratic with a positive discriminant ?  Which belongs to a quadratic with a negative discriminant ?  Which graph has a discriminant equal to zero ?

Without solving, determine the number of real solutions for each quadratic equation. 1.x 2 + 7x + 33 = 8 – 3x 1.x x + 25 = 0 2.(10 2 ) – 4(1)(25) One real solution 2.7x 2 + 2x + 5 = 0 1.(2 2 ) – 4(7)(5) 2.4 – No real solutions 3.2x x = x 2 + 4x x 2 + 6x + 3 = 0 2.(6 2 ) – 4(1)(3) Two real solutions 4.4x = -4x 1.4x 2 + 4x + 9 = 0 2.(4 2 ) – 4(4)(9) 3.16 – No real solutions

State whether the discriminant of each quadratic is positive, negative, or equal to zero. Then identify which graph matches the discriminants below. Graph #2Graph #1 Graph #4 Graph #3