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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.

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