PARABOLAS

Some parabolas open up while others open down. If it opens upwards, the parabola has a minimum ("hold water.") If it opens downwards, it would "spill water," and it has a maximum point. A parabola facing up, is called "concave up." A parabola facing down is called: "concave down."

 Graph the function: Y = - x exp2 + 4x + 3.

Step 1.  Find the x-and the y-coordinate of the vertex of the parabola before constructing a table of values to graph it. The maximum is at (2, 7) this point is the vertex or maximum. Use 1, 0, 3 and 4 as the domain to find the corresponding range values. The formula to find the x coordinate of the vertex is : x = -b/2a. The axis of symmetry passes through the vertex. Note: that there are other ways to find the vertex using another vertex formula which is discussed in more advance math courses. You might want to do research on this. At the moment I am only covering the basic facts. Later in these series I would dedicate sometime to that section. For the moment, some basic facts are enough.

Step 2. Graph the parabola.

Use the quadratic formula to show the roots of the quadratic equation are real numbers. The quadratic formula show that it is, if not impossible, to graph its roots--since the real are infinite in nature and some of the impossible to sketch or graph with any specific certainty. Later we will see how easy it becomes, to graph certain types of quadratic functions. It is a fact of life, one cannot graph some points on a number line ever as their existence belong in Noumena.