Quadratic Relations

Introduction

What is Quadratic equation?

  • A Quadratic equation is polynomial equation of the second degree. The general is

ax^2 + bx + c = 0


  • where x represent a variable or an unknown, and a,band c are constants with a is not equal to 0. (if a= 0 then equation is a linear equation.)



  • The a, b, and c are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term.

Tabel of contents

Table of contents

Graph

Word problems

Vertex form

Finding equation

Factored form

Multiplying Binomials

Common Factoring

Simple Grouping

Factoring Trinomials

Graph

Vertex

Axis of symmetry

Optimal value

Roots

Direction of opening

Vertex

what is vertex?

Each quadratic equation has either maximum or minimum, but did you that this point has a special name? In a quadratic equation, this point is called the vertex. Take a look at the vertex of quadratic equation by looking at this picture.

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Axis of symmetric

What is axis of symmetry?

Ever notice that the left side of the graph of a quadratic equation looks a lot like the right side of the graph? In fact, these sides are just mirror images of each other! If you were to cut a quadratic equation graph vertically in half at the vertex, you would get these symmetrical sides. That vertical line you cut has a special name. Its called the axis of symmetry.

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Optimul value

What is optimul value?

Lets say you are using parabola to define the cost of something as function of some variable. In that case "optimal" would probably be the cheapest value, or the lowest point on the parabola.

Roots

what is roots?

A parabola can cross the x-axis once,twice or never. These points of intersection are known as X-intercepts, zeros or roots.

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Direction of opening

what is direction of opening?

If the value of "a" in equation is positive then parabola opens upward. If the value of "a" is negative then parabola will opens downward.

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Word Problems

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Vertex forms

Vertex form tells us about what the graph look like.

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Finding Equations

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Factored Form

Factored form

  1. The form of an algebraic expression in which no part of the expression can be made simpler by pulling out a common factor. ex. The factored form of the expression x3+x2-2 is x(x+2)(x-1).

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Multiplying Binomials

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Common Factoring

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complex Trinomials

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Factoring Trinomials

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Simple Trinomials

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Difference of square

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Perfect Factoring

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