Quadratic Website

By: Omar Osman

Graphing Using Vertex Form

Learning Goals

what I able to do

-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

Quick Way of Graphing a Quadratic Function in Vertex Form
Graphing Using Graph Transformations - Example 1

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 Equation for this is y=(x-s) (x-r)


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

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

What I learned was standard formula ,how to find the x intercept using the quadratic formula ,how to complete square using vertex form and Discriminant values.

Standard Form

Y=ax²+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

Big image
Finding the x-intercepts using the Quadratic Formula

My Video PT 1,2

May 8, 2016
May 8, 2016

Complete the square using vertex form

Completing the Square and Vertex Form of Quadratic Equations
Discriminant of quadratic equations | Polynomial and rational functions | Algebra II | Khan Academy

Discriminant

To find the d value you must use the formula which is b2-4ac.

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.