Question

What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?

Answer 1

I don't understand how to do this

Answer 2

You are expected to observe the property that the Vertex lies exactly between the Focus and the Directrix. This exposes almost all of the formulation of the parabola.

Answer 3

Okay so what do I do first?

Answer 4

Write down the coordinates of the vertex.

Answer 5

ok

Answer 6

is it (4, -5)?

Answer 7

Exactly in the middle. You have -3 and -6 to work with.

Answer 8

What is the arithmetic mean of -3 and -6? The vertex must be exactly the same distance from each. It's a definition of a parabola.

Answer 9

oh okay

Answer 10

still lost... Im really terrible at math

Answer 11

I doubt that. You can find the average of -3 and -6. "-5" was close. Why did you guess that? Calculate the average.

Answer 12

Um because on your graph it moved two places so I thought it went down 2 and became -5.

Answer 13

Now do the same thing from y = -6. Did it move two places? If not, then you aren't in the middle. Move the SAME distance from -3 and from -6. Where does that put you?

Answer 14

I move it up 1 and it become (-5) as well?

Answer 15

sorry for taking so long I got a phone call from my teacher

Answer 16

Why is moving 2 from -3 and moving only 1 from -6 the same distance? \(2 \ne 1\) Move the SAME distance from each one.

Answer 17

Oh okay let me think. Then do both sides move by 1.5?

Answer 18

Nvm Thanks for trying to help me though...

Answer 19

That's the spirit. \(\dfrac{-3 + (-6)}{2} = -4.5\) Nice.