## Precalc week 11

This week in precalc we continued with graphing inequalities and quadratic functions.

In lesson 5.3 we learned how to graph quadratic functions with two variables instead of one.  the process is almost the same as one variable except we are dealing with parabolas now.

Ex :

$y \textgreater x^2+6x+10$

$= (x+3) -1$

Now using this information we can graph a parabola using the vertex (-3, 1) and the a value of 1.  An extension to this is now we have a inequality so that means we have to shade in part of the graph.  WE know that the parabola is facing up and the inequality sign is less than so that will mean we will have to shade in outside of the parabola.  The line creating the parabola will also be a solid line.

In lesson 5.4 we learned about intersecting inequalities on a graph and how to solve them.  The point where both parabolas or lines are touching each other marks the point of intersection.

Ex :

$y=x^2+5$

$y=-x^2+7$

After graphing these two parabolas, the points of intersection are (1,6) and (-1,6) which is the answer.  Sometimes there can be an infinite amount of points and sometimes there cannot be any points of intersection.