# Dealing with Quadratics!

### Alerbra Guide sheet

## whats a quadratic?

-has the highest degree of 2

-graphed as a parabola

## Different Quadratic Forms

## Standard: (y=ax^2 +bx+c)-reveals little about the parabola -a =determines whether the parabola opens up or down also whether its a vertical stretch or compression. -c =he y intercept (where the parabola touches the y-intercept) -to change into factored you factor and to change into vertex you complete the square. | ## Factored: y=a (x-r)(x-s)-reveals little about the parabola. -a =determines whether the parabola will open up or down or whether it's a vertical stretch or compression. - r,s= reveals the zeros ,x-intercepts (when the parabola will touch the x-axis) -to change into standard you expand and simplify and to change into vertex, from there you complete the square. | ## Vertex: y=(x-h)2 +k-reveals the most about the parabola -a= determines weather the parabola opens up or down and whether its a vertical stretch or compression. -h= x-value of the maximum or minimum (when does it happen?)- the time it takes (left or right). -k= the maximum or minimum (where does it happen?) |

## Standard: (y=ax^2 +bx+c)

-reveals little about the parabola

-a =determines whether the parabola opens up or down also whether its a vertical stretch or compression.

-c =he y intercept (where the parabola touches the y-intercept)

-to change into factored you factor and to change into vertex you complete the square.

## Factored: y=a (x-r)(x-s)

-reveals little about the parabola.

-a =determines whether the parabola will open up or down or whether it's a vertical stretch or compression.

- r,s= reveals the zeros ,x-intercepts (when the parabola will touch the x-axis)

-to change into standard you expand and simplify and to change into vertex, from there you complete the square.

## Vertex: y=(x-h)2 +k

-reveals the most about the parabola

-a= determines weather the parabola opens up or down and whether its a vertical stretch or compression.

-h= x-value of the maximum or minimum (when does it happen?)- the time it takes (left or right).

-k= the maximum or minimum (where does it happen?)

## How to Expand and simplify :

EXAMPLE: the equations seen below is in factored form expand and simplify.equation:y=a(x-r)a(x-s).

step1: First to expand you, apply everything directly in front of the bracket into every term inside the bracket.-y=a(x-r)a(x-s)-y=ax-ar+ax-s.

step2: You collect the like terms to simplify ,meaning collect everything that has the same components. (ex; coefficients,exponents ect)-y=ax-ar+ax-sy=2ax-ar-s.

step3: Leave what ever cannot be collected and simplified and just add them into the equation.

## How to Compleate a Square:

(Ax2+Bx+C)- Referance Equation.step1:Block off the first two terms. 1)y= 2x2+8x-3 then... y= (2x2+8x)-3.

step2: Factor out the A value. 2)y=2(x^2+4x)-3. (note : when you factor out the A you divde the middle term by it.)

step3:To find your zeros didvide te middle term by two the square it .y=2(x2+4x+4-4)-3.

step4:Take the negative out then solve the ending and divide the equation by two. 4)y=2(x+2x)2-11.(note:when you take the negative out multiply it by the first term "A" then take out the positive zero and bring the square root to the end bracket.)

## Quadratic Formula

## Factoring

There are many ways of factoring here are just SOME ways!

GOLDEN RULE:

-always look for a common factor

-then check if it can be factored any more

-Difference of squares.

here is an example: x^2-9 (you would square both terms)

another example is: (x+5)(x-5)

these are the two types!

-Decomposition.

here is an example: 2x^2+5x-7

-start off by solving for the product and the sum for the middle term and replace it: 2x^2+7x-2x-7

-then factor out common terms :x(2x+7)-1(2x+7)

- then simplify even more (2x+7)(x-1)

-By Grouping

here is an example: x^3+2x^2+8x+16

-the first thing to do would be to block off each two terms then factor out what ever is in each bracket x^2(x+2)(X^2+8)

-then factor/simplify the rest! (x+2)(x^2+8)