# Quadratic relations

### By Deepak Gogna

## Topics

Transformation of quadratics

Quadratic relations

Graphing y=(h-k)2+k

factored form- Y=a(x-r)(x-s

special product

multiplying polynomials

common factors

factor quadratic expression of form x2+bx+c

factor quadratic expression of form ax2+bx+c

factor a perfect square trinomial and difference of squares

maxima and minima

solve quadratic equations

graph quadratics using the x-intercept

The quadratic formula

solving word problems using the quadratic formula

## What is quadratics?

Factored form is : y= a(x-r)(x-s)

Standard Form is : y =ax2 + bx + c

A quadratic relationship is shown by a parabola.

You can tell if its a quadratic by first and second differences.

## Transformation of quadratics

Transformations:

The (-h) moves the vertex of the parabola left or right

The (k) moves the vertex of the parabola up or down

The (a) stretches the parabola and if the

Vertex= (h,k)

Once the vertex of a parabola is indicated the step pattern is used to find the rest of the points.

## optimal value

## complex factoring

The different about complex factoring is that it does not have a coeffiecient of 1 and there are no common factors.

An example is :

4x^2 +6x + 4

## common factoring

First take out all common factors in equation

Also take out any common variables

Mission is to take out all common factors

## simple factoring

## Perfect Squares

A perfect square is a square of a whole number, a number that is squarable.

A perfect square's equation looks like

a^2 + 2ab +b^2

## difference of squares

A difference of squares equation looks like...

a^2 - b^2

## The quadratic formula

Step 1: Find the coefficients a , b and c

Step 2: Plug in the values for a, b, and c into the quadratic formula

Step 3: Simplify

Step 4: Solve for X

## step pattern

## Maxima and Minima

Maxima and minima are the lowest or highest

points on a parabola. When the vertex is the lowest point on the parabola

then it is know as the minimum value. Also If the vertex is at the highest point on

the parabola then it is know as the maximum value.

## Multiplying polynomials

## Connections

When you are changing standard form into vertex form you have to use factoring

Lastly When you are converting vertex form into standard form you have to use expanding and simplifying