This week in Pre-Calc we learned about Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, and Solving Quadratic Systems of Equations.

When solving in one variable you first factor the expression, then Determine the zeros, and then using a sign chart (number line) determine your restrictions etc.

When graphing linear inequalities in two variables it is represented by a boundary line and a shading on one side. The boundary line can be a solid line/broken line. If solid it means it is greater than or equal to, and if it’s broken that means it is either less than or greater than. To graph an inequality first graph the equation, then determine whether you have a solid or broken line. Next choose a test point not directly on the line. When you can use (0,0), if the statement at the end is true, shade that side of the line, if not  shade the other side. Always isolate y

When solving Quadratic Systems of Equations you would solve algebraically, either with substitution, or elimination. You could also graph, but if your point of intersection is not on a “pretty” point, you will not be able to be completely accurate. To solve get everything equal to zero.

Systems: What is a system? A system is when 2 or more equations are needed to find a solution. Their point of intersection is the solution. If 2 lines are parallel they will never have a solution. If the lines are the exact same and are right on top of each other there is an infinite number of solutions. The 3 types of solving systems is graphing, elimination, and substitution.