Quadratic Relations Guru

Know everything there is about Quadratic Relations here!

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Why do we need Quadratics in our life?

"Why do we need Quadratics in our life?". This question is frequently asked by students all around the world. Quadratics can be used for so many different things! With quadratics, you can graph the flight path of an object. For example, if you throw a ball into the air and want to know what time it will fall to the ground, you would use Quadratics.

Table of Contents

As you read through this website, there are 3 main forms that you will learn about. Everything else evolves around these three important forms in Quadratics.

  1. Standard Form

  2. Factored Form

  3. Vertex Form

Equation #1 - Standard Form: ax² + bx + c

The Standard Form of a Quadratic Equation looks like this:
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2x2 + 5x + 3 = 0

2 = a, 5 = b, 3 = c


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Axis of Symmetry

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Completing the Square

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How to Factor?

Common Factoring

Common Factoring Tutorial

Factoring Simple Trinomials

Factoring Simple Trinomials

Factoring Complex Trinomials

Factoring Complex Trinomials

Equation #2 - Factored Form: y=a(x-r) (x-s)

(x – 3)(x – 4)

a = 1, r = -3, s = -4
A quadratic relationship can have one root (touches down on the x-axis only once), two roots (crosses through the x-axis in two places) or no real roots (never crosses the x-axis).
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Graphing Using Factored Form

3.5 Graphing from Factored Form

Equation #3 - Vertex Form: y = a(x - h)² + k

h is the 'x' value and k is the 'y' value


A - Vertical stretch/ compression

K - Vertical translation

H - Horizontal translation

Hint: If your a value is a negative number, your parabola will flip and face downward. This is called a Vertical Reflection.

Graphing Using Step Pattern

3.3 More Graphing from Vertex Form