# Quadratic Website

### By: Omar Osman

## Graphing Using Vertex Form

## Learning Goals

-put equations in graphs

- put parabola in graphs.

## Vertex Form

**y=a(x-h)²+k**

** The H,K is the Axis of symmetry. which means that H is the X value and K is the Y value.**

**The A values tells you the direction the the parabola. The way to tell the directions if it's negative it's facing downward and if it's positive then facing upward. It also tells you whether the parabola is going to be compressed or stretched. **

**The K represent the vertical shift. So how far up or down the graph has shifted. **

**The H value represents the horizontal shift. So how far left or right the graph has shifted.**

## Links to videos

## Quadratics- Factored form

## Learning goals

· Expanding and simplifying

· Monomial Factoring (GCF)

· Binomial Factoring (GCF)

· Factoring by grouping (4 terms)

· Simple trinomial factoring

· Complex trinomial factoring

· Special Product- Difference of Squares

· Special Product- Perfect Square Trinomial

· One Application problem

· Graphing by factored form

· Factored form equation

· Finding vertex and axis of symmetry in factored form

## Factored Form

The value gives you the shape and the direction of the opening.

The r and s value gives you the x intercept.

## Expanding and Simplifying

(x+9)(x+5)

=x²+5x+9x+45

=x²+14x+45

I multiplied each term in the bracket with both other terms in the other bracket.

Then I added the common terms.

**Factoring**

Monomial factoring:

(5x+5)

=5(x+1)

I took out the common factor

Binomial Factoring

3x(x+5)+2(x+5)

=(3x+2)(x+5)

I combined the common bracket and put the remaining terms in a bracket

Factoring by grouping

12x²+6x+4x+2

6x(2x+1)+2(2x+1)

(6x+2)(2x+1)

I found the GCF for each pair of brackets

Simple trinomials:

x²+7+10

(x+5) (x+2)

complex trinomials:

3x²+8x+5

3x²+3x+5x+5

(3x²+3x)(5x+5)

3x(x+1) +5(x+1)

(3x+5) (x+1)

Difference:

x²-25

(x-5) (x+5)

Perfect square:

x²+6x+9

app problem:

The area of the rectangle is x²+15+56, find the length and width.

Product= 56

Sum= 15

(x²+7x)(8x+56)

x(x+7)+8(x+7)

(x+7)(x+8)

there fore the length is (x+7) and the width is (x+8)

## Part: 3 Standard Form

## Learning Goal

## Standard Form

**Y=ax**

**²**

**+bx+c**

The value of "**a**" gives you the shape and the direction of the opening.

The value of "**c" **is the y intercept.

## Quadratic Fromula

## My Video PT 1,2

## Complete the square using vertex form

## Discriminant

You are suppose to sub in your standard form in your equation.

If answer you get is above zero the there's 2 solution. If the answer is equal to zero then there's one solution and if it's less than zero then there's no solution.