Introduction to Quadratics
The Three Formulas
The three formulas used in this chapter will be:
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Discriminant
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Quadratic Formula
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Completing the square
Discriminant
Finding the discriminant allows you to find out how many X-intercepts you will have. The equation to finding the discriminant is:
y=b^2-4ac.
If you have an answer that is less than 0, that means that there will be no x-intercepts.
If your answer is greater than 0, that means that you will have two x-intercepts, and if your answer is 0, you will have only one x-intercept. Finding the discriminant is a helpful equation because it gives you information about how many x-intercepts you will have. This equation can only be used when you have the Standard Form of a Parabola.
Quadratic Formula
The Quadratic Formula is a way for you to get the actual X-intercepts. The Quadratic formula is similar to factoring by DECOMP in the sense that both ways will give you the X-intercept. The equation to do this is:
Maxima and Minima
Completing the square is a formula that allows you to convert a Standard form equation into Vertex form. There is no correct equation to convert Standard form to Vertex form. Instead you will need to follow a sequence of steps. If a is negative it will give you the maximum value. Also, if a is positive then it will give you the minimum value.
