# New Quadratics

### The new and improved way to learn Quadratics

## What to be prepared for

## Standard Form Quadratic

** y** =

*a*(*x*-*h*)2 +*k what does this mean?*- If
0, the quadratic will open downwards.*a*< - If
0, the quadratic will open upwards*a*>

*If you increase the a value the arms will grow larger. *

*The (h,k) will always be the coordinates of the minimum and maximum values *

## The list on what to do.

## New Topic Vertex form

## Parabola

The Parabola is what happens to the graphing a Quadratic Relation- containing very important segments that come together to create a Parabola:

Vertex which is where the parabola and the axis of symmetry meet: (x,y)

Axis of Symmetry which divides the parabola equally: (x=#)

X-Intercept is also known as (zeroes/all real numbers) is where the line passes through the x axis: (#,0)

Y-Intercept where the line passes through the y axis: (0,#)

Optimal Value is the Y coordinate of the Vertex and the Optimal Value is also the highest or lowest point: (y=#)

## Factored form

## Factoring

## Converting From form to form

## Converting vertex form to factored form

To convert from Vertex form to factored form

1. Change y as 0

2. Place k value over the equal sign

3. Divide "a" value form both sides of equation

4. Square root both sides so you can get rid of the square root on the right side

5. Finally move your "h" value over the equal sign

## Converting Standard form to vertex form

1. Remove the common factor from the x^2 and the x term(coefficient)

2. Locate the constant that must be added and subtracted to create a perfect square. Rewrite the expressions by adding and subtracting the constant

3. group the three terms that form the perfect square ( move subtracted value outside the brackets by multiplying it by the common factor fist )

4.factor the perfect square and collect all like terms

## Zeroes

*x*-axis once, twice, or never. These points of intersection are called

*x*-intercepts or zeros.

## optimal value

## Axis of Symentry

## Word problem finding the answer

**The product of two consecutive negative integers is****1122****. What are the numbers?**

Remember that consecutive integers are one unit apart, so my numbers are *n* and*n* + 1. Multiplying to get the product, I get:

*n*(*n* + 1) = 1122 *n*2 + *n* = 1122 *n*2 + *n* – 1122 = 0

(*n* + 34)(*n* – 33) = 0 Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved

The solutions are *n* = –34 and *n* = 33. I need a negative value, so I'll ignore "*n* = 33" and

take *n* = –34. Then the other number is *n* + 1 = (–34) + 1 = –33.

**The two numbers are ****–33**** and ****–34****.**

Note that the second value could have been gotten by changing the sign on the extraneous solution. Warning: Many students get in the very bad habit of arbitrarily changing signs to get the answers they need, but this does not always work, and will very likely get them in trouble later on. Take the extra half a second to find the right answer the right way.

## Word promblems

## Cool things to know

## Math in words

**There was a negative Boy, who was confused about whether or not he should go to a radical party. The Boy was square, so he missed out on 4 Awesome Chicks and he cried until the party was over at 2 Am.**

Hint: x=[-b +/- sqrt(b^2-4ac)]/2a

A: Parabolas (pair of bolas)

A : Because they have sine and cosine to get a tan and don't need the sun!