Dealing with Quadratics!

Alerbra Guide sheet

whats a quadratic?

-has the highest degree of 2

-graphed as a parabola

Different Quadratic Forms

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

The quadratic formula can help you to find your x- intercepts or the roots as long as the format is in (Ax2+Bx+C).
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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)