In week 12 we did a lesson on solving Quadratoc systems of equations. Just by looking at the graph we can tell how many solution it will have.

In order to solve quadratic systems of equations you need to use substitution.

Ex:

x-2y=-10

3x-y=0

isolate one of the variables

3x=y

 

put 3x into y

x-2(3x)=-10

x-6x=-10

-5x=-10

x=2

put ^ (x=2) back into the equation to find y

2-2y=-10

-2y=-12

y=6

answer: (2,6)

 

 

This week we started looking at solving Quadratic Inequalities in 1 variable.

In order to solve quadratic inequalities we need to find the zeroes of the functions. To find the zeroes of a function we need to factor.

For example;

we can factor that into; (x+4)(x-2)>0

the zeroes of the function are; -4 and 2

 

from finding the zeroes of the function we can determine what numbers x can be to make it positive or negative.

To find if what x needs to be, you place both the zeroes of the function on a number,one and substitute a number in x three time. One needs to be less than -4 (lowest zero pair)  another one needs to Ben more than 2 (greatest zero pair) and he third numbers needs to be in between -4 and 2. By solving the equations we can figure out what x has to be greater than and less than.

In this case  the solution for the inequality is; x<-4 and x>2