Quadratic Functions, Quadratic Expressions, Quadratic Equations

Slides:

Advertisements

Similar presentations

Factor and Solve Quadratic Equations

Advertisements

Quadratic Functions, Quadratic Expressions, Quadratic Equations

Solving Quadratic Equations by Graphing

Adapted from Walch Education  The standard form of a quadratic function is f ( x ) = ax 2 + bx + c, where a is the coefficient of the quadratic term,

Quadratic Equations Algebra I. Vocabulary Solutions – Called roots, zeros or x intercepts. The point(s) where the parabola crosses the x axis. Minimum.

1Higher Maths Quadratic Functions. Any function containing an term is called a Quadratic Function. The Graph of a Quadratic Function 2Higher Maths.

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.

Drill #92 Identify the maximum or minimum value of each quadratic function, then state the domain and range of each.

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.

JEOPARDY! Graphing Quadratics Graphing Solving using Square Roots Discriminants GO TO FINAL.

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.

5.5 Quadratic Formula Warm-up (IN) Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find.

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.

Quadratic Functions. How Parabolas Open A parabola will open upward if the value of a in your equations is positive-this type of parabola will have.

5.5 – The Quadratic formula Objectives: Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate.

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.

Graphing Quadratic Equations

Graphing Quadratic Functions (2.1.1) October 1st, 2015.

Reminders (1) The graph of a quadratic function is a parabola. If a > 0 the parabola isshaped and the turning point is a minimum. If a < 0 the parabola.

2.1 – Quadratic Functions.

Roots, Zeroes, and Solutions For Quadratics Day 2.

Solving Quadratic Equations by Graphing 4 Lesson 10.2.

$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.

Complex Numbers FactoringGraphing Quadratic Function Vocab 200.

Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing  DESCRIBE the Elements of the GRAPH of a Quadratic Equation  DETERMINE a Standard Approach.

Graphing quadratic functions part 2. X Y I y = 3x² - 6x + 2 You have to find the vertex before you can graph this function Use the formula -b 2a a = 3.

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

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

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.

Solving Quadratic Equations by Graphing Need Graph Paper!!! Objective: 1)To write functions in quadratic form 2)To graph quadratic functions 3)To solve.

Section 2.5 – Quadratic Equations

Factor each polynomial.

How To Graph Quadratic Equations Standard Form.

Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations Discriminants of Quadratics Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.

Solving Quadratic Equation by Graphing

Introduction to Quadratics

Introduction The equation of a quadratic function can be written in several different forms. We have practiced using the standard form of a quadratic function.

Quadratic Functions and Their Properties

Quadratic Equations Chapter 5.

Using The Discriminant

Discriminant Factoring Quadratic Formula Inequalities Vertex Form 100

6.2 Solving Quadratic Equations by Graphing

Solving Quadratic Equation and Graphing

Solutions, Zeros, and Roots

Y Label each of the components of the parabola A: ________________ B: ________________ C: ________________ C B B 1 2.

Solving Quadratic Equations by Graphing

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

Solving a Quadratic Equation by Graphing

Completing the square means writing the unknown terms of a quadratic in a square bracket Example because Application To find the maximum or minimum value.

Quadratic Functions.

E) Quadratic Formula & Discriminant

3.1 Quadratic Functions and Models

Graphing Quadratic Functions (2.1.1)

Quadratic Functions The graph of a quadratic function is called a parabola. The parent function is given as This is the parent graph of all quadratic functions.

Solving Quadratic Equations

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

The Discriminant CA 22.0, 23.0.

Review: Simplify.

Solving Quadratic Equation

Day 146 – Solve

3.1 Quadratic Functions and Models

Warm-Up 6 minutes Use the distributive property to find each product.

Algebra 2 – Chapter 6 Review

Quadratic Equation Day 4

QUADRATIC FUNCTION PARABOLA.

Effect of the Real Numbers h and k of a

How To Graph Quadratic Equations.

Presentation transcript:

Quadratic Functions, Quadratic Expressions, Quadratic Equations Definition: A quadratic function is a function of the form where a, b, c are real numbers and a  0. The expression on the right-hand-side is call a quadratic expression.

Quadratic Expressions: Factored Form Examples: 1. 2.

Factoring quadratic expressions: Given where a, b, c are integers. Case 1: a = 1; Since

we have

Examples:

Case 2: where a, b, c are integers and a  1. Since

we have

Examples:

Quadratic Equations: A quadratic equation is an equation of the form: Problem: Find the real numbers x, if any, that satisfy the equation. The numbers that satisfy the equation are called solutions or roots.

Methods of Solution: Method 1: Factor then the solutions (roots) of the equation are

Examples:

Method 2: Use the QUADRATIC FORMULA The real number solutions (roots) of the quadratic equation are: provided Method 2: Use the QUADRATIC FORMULA

The quadratic formula is often written as The number is called the discriminant.

The Discriminant: Given the quadratic equation If:

(1) ; the roots are: (2) the roots are: (3) no real roots.

Examples:

Quadratic Functions: The graph of is a parabola. The graph looks like if a > 0 if a < 0

Key features of the graph: The maximum or minimum point on the graph is called the vertex. The x-coordinate of the vertex is:

The y-intercept; the y-coordinate of the point where the graph intersects the y-axis. The y-intercept is: The x-intercepts; the x-coordinates of the points, if any, where the graph intersects the x-axis. To find the x-intercepts, solve the quadratic equation

Examples: Sketch the graph of vertex: y-intercept: x-intercepts:

Sketch the graph of Vertex: y-intercept: x-intercept(s):

Sketch the graph of Vertex: y-intercept: x-intercept(s):