The definition of a parabola is the set of all points that are equidistant to a focal point and a line called a directrix. Howver, it is best recognized by its classic u-shape.
Parabolas either open up, down, right, or left. The graphic below will show you how a parabola looks in comparison to its equation.
When the x-value is being squared, the parabola opens up when the p-value is positive and down when the p-value is negative.
On the other hand, when the y-value is being squared, the parabola opens right when the p-value is positive and left when the p-value is negative.
The h-value and the k-value represents the location of the vertex, V(h,k). Therefore, it is important to know the location of the vertex in order to determine the exact equation of a parabola. Conversely, when the equation of a parabola is known, the exact location of the vertex can be determined.
Here is a video and a quiz that will help you understand and assess your understanding of parabolas.
Here are activities related to the lessons above.
ctivity: Conics: Supplemental
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esson: Characteristics of Parabolas