This week in math class we learned more about graphing quadratic systems of equations.

We learned how to graph a quadratic-linear system as well as a quadratic-quadratic system. There are many ways to graph these in order to get 0, 1, 2 or infinite solutions. Here are some examples.

These systems can also be solved algebraically, through substitution.

example:

2x+y=4

2y+3x=0

Let’s take 2x+y=4

y=4-2x

now let’s substitute in y in the other equation.

2(4-2x)+3x=0

8-4x+3x=0

-x=-8

x=8

We now know what x fro our solution is. In order to find the y at the solution, we simply can add in the value of x in either of the equaitons

y=4-2x

y=4-2(8)

y=4-16

y=-12

This is what it looks when it is graphed, and I know that my solutions were right.

This week we also learned about absolute value functions, and what happens when we graph them.

Simply taking y=x, it becomes very clear what happens when we graph y=x and when we graph y=|x|.

If, for example the x was negative, then the y would be negative. When |x|, this means that x will always be positive, and therefore it will not go down into the negative zone, but simply bounce right up. Here is an example of a linear equation.

 

And here is an example of a quadratic equation. Wherever the value of the parabola was negative, it will become positive when the absolute value of it is graphed, and therefore it will simply flip up, or be reflected.