Posted on

# Week 12 in PreCalc 11

We dealt with a lot of things this week, especially about systems. And for this blog, I’m going to talk about linear-quadratic system.

Let’s have a quick recap:

• Linear equation deals with a straight line on the graph. Basically, an equation of a line.
• The equation being known as y = mx + b, where is the slope, and is the y-intercept.
• Quadratic equation deals with a parabola on a graph, with the equation having at least one squared variable.
• The standard equation being known as y = a (x – p)2 + qFind out more on my blog post about quadratic equations!
• Together, they form a relation called System of Linear and Quadratic Equation.

Systems (where they intersect) of these two equations can be find out or solved:

• graphically.
• algebraically.
• substitution.
• elimination.

However, in this blog I’m only going to talk about solving it graphically.

(At this point, you should be able to graph both of them!)

NOTE: There are three possible cases that can happen if you finished graphing them!

(graphs used are in courtesy of desmos!)

• Two solutions – if the line passes on two points of the parabola
• One solution – if the line passes only on one point of the parabola.
• No solution – if the line and the parabola doesn’t cross at all.