In week 8 of precalc, we went over review on the quadratic formula, then went over discriminant, then we went over graphing. A quick definition of the discriminant is the

√b^2 -4ac part of the quadratic formula. The point of a discriminant is that it will help you know how many answers you will get. If the discriminant is over zero you will get 2 different answers. An x1 and an x2. If it is zero then you will get only 1 answer. If it is less than zero you will get no answers because you can’t root a negative. Basically, finding the discriminant will help you know if there is a solution and how many in a fast way.

On to graphing, graphing is relatively easy. Making the T chart is the hard part. In a standard graph there are X and f(x)/Y values. The X values are known as the input and f(X) or Y is the output. So far, we have learned about quadratic functions (Y=X^2) and linear functions(Y=X). We have been doing equations in which we find f(x) or Y to see how the input and output values work. Lets use this quadratic function equation as an example.

f(X)=-X^2

This might seem simple but a mistake I made was forgetting the order of operations and making f(X) positive as I thought it was a trick question and a negative number squared is positive. I was supposed to be squaring, then making it a negative.

Now with this equation we start by making a T chart

After making the T chart, we put dots on the graph in the position indicated by the numbers we have, such as (X3,Y-9) and (X0,Y0) and so on. After putting in the dots, we connect the dots with a straight line, for this type of equation, the lines will usually be drawn going out of the chart. Furthermore, for this specific equation I decided to leave in the parent equation for quadratic functions (in blue) with the equation we used as an example (in red) to see what has changed.

That is pretty much the basics about graphing quadratic functions and what a discriminant is.