
Quadratic EquationsDefinitionax^{2} + bx + c = 0 a, b, c are constants (generally integers) RootsSynonyms: Solutions or Zeros
Consider the graph of quadratic equations. The quadratic equation looks like ax^{2} + bx + c = 0, but if we take the quadratic expression on the left and set it equal to y, we will have a function: y = ax^{2} + bx + c When we graph y vs. x, we find that we get a curve called a parabola. The specific values of a, b, and c control where the curve is relative to the origin (left, right, up, or down), and how rapidly it spreads out. Also, if a is negative then the parabola will be upsidedown. What does this have to do with finding the solutions to our original quadratic equation? Well, whenever y = 0 then the equation y = ax^{2} + bx + c is the same as our original equation. Graphically, y is zero whenever the curve crosses the xaxis. Thus, the solutions to the original quadratic equation (ax^{2} + bx + c = 0) are the values of x where the function (y = ax^{2} + bx + c) crosses the xaxis. From the figures below, you can see that it can cross the xaxis once, twice, or not at all.

