# Quadratic Relations

## About Quadratics

Quadratics is an quadratic equation. This is related to a parabola which is a variable raised to the second power. This can not be raised more then the second power or else this is not a quadratic equation.

## Unit One: Learning Vertex Form

In this unit you will be learning how to graph vertex form, learn to create the equation of vertex form and also about step patterns. To graph vertex form step patterns are required to calculate the parabola's curve. Creating the equation of a vertex form is done by using the equation y=a(x-h)^2 + k. "a" telling the direction of opening and also weather the parabola is stretched or compressed. "h" is the horizontal translation and "k" the vertical translation. Step patterns are calculated by the x and y axis. for example if x is 1 and y is one then x is 2 and y is 4 the step pattern is "x"*2.

## Graph example

This example shows how vertex h and k are represented. Even though "h" is negative 3 it is shown as positive three on the graph and that is because it gets flipped. If the equation was "y=(x+3)^2+2" the vertex would be (-3,2). This is only for the x axis not for the y as it remains the same.

## Word Problem

The path of a football is modeled by the relation h=-1/4(d-12)^2+36 where is the horizontal distance, in metres, after it was kicked, and h is the height, in metres above the ground.

a)What is the maximum height of the football?

b)What is the horizontal distance when this occurs?

## Unit Two: Learning Factored Form

## Learning Goals and Summary

Learning goals for this unit include solving and recognizing different factored forms and also drawing a graph and identifying its "x" and "y" intercepts. The factored form equation is y=a(x-r) (x-s). The "a" shows the direction of the parabola opening and weather it is stretched or compressed. The "r" and "s" values are representing the "x" intercepts. Their are different types of factoring, they include Greatest Common Factor, Simply Trinomials, and Complex Trinomials

## Unit Three: Learning Standard Form

## Learning Goals and Summary

In this unit we will be learning how to change the equation of y=ax^2 +bx+ c into y=a(x+h)^2+k and finding x intercepts of the parabola. To change the equation from Standard form in to vertex form completing the squares is required. Solve by using the quadratic formula for finding the x intercepts.