Parabola intuition 3

The  exercise appears under the Algebra II Math Mission. This exercise practices analyzing information about a parabola.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the focus and directrix, then write the equation: This problem has a graph of a parabola. The student is asked to move the focus and directrix on the graph to make the correct graph of the given parabola, then write the equation of the parabola based on this manipulation.Parint3.png

Strategies
Knowledge of all the conics are encouraged to ensure success on this exercise.
 * 1) The vertex of a parabola can be found by analyzing vertical and horizontal shifts from the parent graph.
 * 2) The focus and directrix are equidistant from the vertex, the focus being "inside" the cup and the directrix outside.
 * 3) This problem can be moved until the equation matches up, ensuring accuracy.

Real-life Applications

 * 1) Conics have uses in optics, for making mirrors to reflect light, and acoustics, to amplify sounds.
 * 2) Conics model motion of celestial bodies due to laws of physics.
 * 3) Satellite dishes are designed with parabolas to reflect rays to a point at the focus.
 * 4) Solar ovens are made with parabolic reflectors.