Question

Chelsea is trying to find the equation of a quadratic that has a focus of (1, 3) and a directrix of y = −3. Describe to Chelsea your preferred method for deriving the equation. Make sure you use Chelsea's situation as a model to help her understand.

Answer 1

If the directrix is at y = -3 and the focus is at (1, 3), what do you know about the vertex?

Answer 2

I honestly have no idea.

Answer 3

Oh boy. Are you familiar with what type of a quadratic this is and what it looks like?

Answer 4

I suck at/hate math but yes.

Answer 5

So what is it? The graph? What does it look like?

Answer 6

The parabola opens up

Answer 7

Very good. Now if I were you, I would take out a sheet of graph paper and plot the focus and the draw the directrix. Can you do that? It will help you tremendously!

Answer 8

Got it

Answer 9

Is that what yours looks like? (Mine is quite skewed without the benefit of graph paper!)

Answer 10

Yes, just straight lol

Answer 11

gotcha!! Do you know where, in relation to the focus and the directrix, where the vertex lies? Do you know the line of symmetry?

Answer 12

axis of symmetry= 1

Answer 13

x = 1, right. What about the vertex? What is its coordinates?

Answer 14

Well the focus is (1,0) what would that make the vertex?

Answer 15

Actually, re-read your problem. The focus is at (1,3). The vertex is at (1, 0). Do you know why?

Answer 16

Well that clears my confusion up lol

Answer 17

Does it? Completely? Do you know how to proceed from here or do you still need some assistance?

Answer 18

I need assistance, What do I tell Chelsea lol

Answer 19

Tell Chelsea to pay attention in class; you have your own problems! LOL!!!!!!!