SOLUTION: I would really appreciate you help. I have to write the equation in vertex form and tell whether it opens up or down. 1. The vertex of the parabola is the (3,-2). Point F (-2

Algebra ->  Rational-functions -> SOLUTION: I would really appreciate you help. I have to write the equation in vertex form and tell whether it opens up or down. 1. The vertex of the parabola is the (3,-2). Point F (-2      Log On


   

Question 522226: I would really appreciate you help.
I have to write the equation in vertex form and tell whether it opens up or down.
1. The vertex of the parabola is the (3,-2). Point F (-2,-8) lies on the graph of the parabola.
Thank you so much
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Since you are concerned with whether the parabola opens up or down I have to assume that the axis is a vertical line. You don't say so, and there really is no other clue about the orientation of your parabola. When you are writing descriptions of things, do not assume anything. Had you stated that you wanted to derive a function whose graph was a parabola, that would have been a different thing.

The vertex form for a vertical axis parabola is:



Where are the coordinates of the vertex.

So:



Is true for this parabola, and if the point is indeed on the graph, then the following must be true as well:



Which is to say:



And the full vertex form equation becomes



Parabolas with a negative lead coefficient open downward. This makes sense upon examining the two given points. The vertex of any parabola function is either a minimum or a maximum. Hence, if the value of the function (the -coordinate) at any point other than the vertex is less than the value of the function at the vertex, the vertex must be a maximum and that means the parabola must open downwards. -8 is less than -2 QED.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism