Sasha and Keoni examine the different equations they derived for parabolas with a p-value of 3 and a vertex not at the origin. By noticing patterns between the location of the vertex and the equation for the parabola, they make a prediction for the general equation of a parabola with a vertex at (h, k) and an unknown p-value.
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 3:43]. What is a general equation of a parabola with a vertex at the origin and a focus placed at a distance of p away from the origin?
2. [Pause the video at 6:55]. What method did Sasha use to locate the focus above the vertex? Why not just count boxes?
Focus students’ attention on precision of language by attending to Sasha’s justification:
1. Sasha provides some justification for why the location of the focus and directrix of the parabola with a vertex of (9, 13) and a p-value of 5. Can someone revoice her ideas?
2. Keoni and Sasha made a conjecture for a general equation of a parabola with a vertex at (h, k) and an unknown p-value? Can someone revoice their conjecture?
1. What would be the location of the focus and directrix of a parabola with a vertex at (–3, 5) and a p-value of 7? Explain how you know.
2. A parabola has a focus at (4, 9) and a directrix of y = 5. What are the coordinates of the vertex of the parabola? How do you know?