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 m is the slope, and b 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 + q. Find 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:
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.