Quadratics Summary

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  • Created by: qmfpp
  • Created on: 10-10-14 17:34

Factorising: Easy Method

x2+bx+c = (x+y)(x+z)

x is not a variable.

z+y=b

zy=c

Example:

x2+bx+c = (x+y)(x+z)

x2+7x+10 = (x+5)(x+2) - [5+2=7, 5x2=10]

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Factorising: Hard Method

ax2+bx+c=(dx+y)(ex+y)

x is not a variable.

zy=c

de=a

Usually d and e, and y and z are close together: e.g. 6x2= 3x, 2x; rather than 6x, x

Example:

2x2+ x -2 = (2x-2)(x+1)  [ this equals 2x2-2]

 = (2x-1)(x+2)

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The Quadratic Formula

For SOLVING equations only!

When ax2+bx+c=0, and a is not equal to 0:

x=(-b±√b² -4ac)/2a

b² -4ac is the discriminant:

- if it is 0, the quadratic only has 1 solution.      

- if it is positive, there are 2 solutions

- if it is negative, there are NO solutions

 - if it is a square number, there are 2 integer solutions

    

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Completing the Square

x² + bx +c

1. (x    )² - ( )² +c

2. Halve b.

3. (x+(b/2))² - ( b/2)² +c

4. If it is an equation, solve.

Parabolas

To find the minimum point:

(x+(b/2))² -(b/2)² +c

-1(b/2) = x co-ordinate

-(b/2)² +c = y co-ordinate

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