Did you know that the graph of a quadratic function is a U shaped curve called a parabola?
You are in College and you are learning about Parabolas for the first time. It's making no sense to you. To top it all, your internal assessments are 2 weeks from now.
Here's a short course which will make Parabolas easy for you.
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Why is a Parabola called a Conic?
You will first learn how Parabolas originated from Conics and the difference between a Parabola, Ellipse and Hyperbola.
Relation between a parabola and conics
A Parabola is the set of all points in a plane equidistant from a fixed point and a fixed line. The fixed point is called the focus and the fixed line is called the directrix. Problems on these are illustrated below.
Simple problem on Parabola
Basic types of Parabolas and how to remember them.
Next, you will learn the 4 basic types of Parabolas. Left, Right, Top and Bottom, as I tell my students. You will learn how to calculate the equation of the axis, the directrix and the focus for each type. The following image illustrates what you need to remember for the 1st form.
Parts of a parabola
You'll learn how to solve problems on all these forms in this course.
What happens when the vertex is not the origin?
What you need to do is to complete the square of the 2nd degree term and you will get the vertex as (x - h, y - k). In this case, you need to remember that the x axis is shifted h units to the right and the y axis is shifted k units on top.
On the other hand, if the vertex is (x + h, y + k), the x axis is shifted h units towards the left and the y axis is shifted k units downwards. You'll need to use this while doing curve sketching in Integration. The following problem illustrates this.
problem on shifting of origin