Access Point #: MAFS.912.G-GPE.1.AP.2aArchived Access Point

Essential Understandings

Concrete:

• Identify objects that have the shape of a parabola, half an egg, satellite dish and the path the water is making out of the fountain.
  
  
• Throw an object in the air and draw a picture of the path the object takes. Click Here

• Understand that a parabola is set of all points in a plane which are an equal distance away from a given point and given line (illustrated by the blue lines in the diagram below). The point is called the focus of the parabola, and the line is called the directrix.
  
  
• Understand that represents the vertical parabola and represents the horizontal parabola.
• Identify what the variables represent in the formula.
• Understand that the vertex is the midpoint between the focus and the directrix that can be found using the formula y=k-a where y is the directrix, a is half the distance from the focus to the directrix and k is the y value of the vertex. For example: given a focus of (1,0) and a directrix y=-2, the distance between the focus and the directrix is 2. The distance from the focus to the vertex is 1. The directrix y=-2 is added to the distance from the directrix to the vertex, -2+1=-1. The y value of the vertex =-1. The x value of the vertex is the same as the focus x value, 1. The vertex of the parabola is (1,-1).
• Understand that given a graph a student can count the distance between the focus and the directrix. When this distance is divided in half it gives you the distance to the vertex, (a).
• Understand that the vertex is a point represented by an ordered pair (h,k). Understand that the x value from the vertex represents h and the y value from the vertex represents k.
• Understand that parabolas can open vertically and horizontally. Parabolas that open horizontally have a directrix with an x instead of a y. The formula for the directrix of a horizontal parabola is x=h-a. The y value of the vertex is identical to the y value of the focus.
• Substitute values into the equation for a parabola. For example: Given a parabola with a focus (1,0) and a directrix of y=-2. The distance between the vertex and the directrix = 1.
  h = 1, k=-1 from the vertex (1,-1)