Equation of a Parabola Based on Its Focus and
The Lesson Activities will help you meet these educational goals:
Content Knowledge—You will derive the equation of a parabola given a focus and
Mathematical Practices—You will make sense of problems and solve them.
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Write a response for each of the following activities. Check the Evaluation section at the end
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Deriving the Equation of a Parabola Given a Focus and Directrix
The vertex form of the equation of a vertical
is given by
) is the vertex of the parabola and the absolute value of
is the distance
from the vertex to the focus, which is also the distance from the vertex to the directrix.
You will use the GeoGebra geometry tool to create a vertical parabola and write the
vertex form of its equation. Open
, and complete each step below. If you
need help, follow these
for using GeoGebra.
Mark the focus of the parabola you are going to create at
(6, 4). Draw a horizontal
line that is 6 units below the focus. This line will be the directrix of your parabola.
What is the equation of the line?