Question 943039: So I'm trying to graph a parabola. I already have an equation for it, I just need to find the vertex, and two other points and then graph it. The equation given is x^2 +3y=0....I have no idea what to do next? Please help! Thank you!
Found 2 solutions by MathLover1, KMST:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
since the vertex form of parabola is  where  and  coordinates of the vertex, if we compare it to we see that  ,  and  ; so, the vertex is at origin ( ,)
make table:
 ,
,
 , .......
 , .......
 , .......
 , .......
plot points and draw a line through:
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! The graph of a parabola looks like this  or like this  .
First, solve for :
<--> <-->
That lat equation allows you to calculate points easily:
you pick a value for 
(for example, for  ,  ).
Looking at that equation, you realize that:
for  ,  , and
for  (negative or positive),  and  .
That tells you that the graph looks like this:
 It has a maximum at  , the origin,
and all the other points are below the x-axis, with  .
In general a parabola with vertex at  has an equation of the form
 <--->  <--->  .
You may be told that it is a quadratic function of the form  ,
but that is the same thing,
with  and  .
In any case, you can find , the x-coordinate of the vertex,
by changing the sign of the coefficient of the term in ,
to get  ,
and dividing by  , twice the coefficient of the term in  ,
to get  .
After that, you just plug that value of into the equation and find ,
the y-coordinate of the vertex.
For example,
 has  and  .
The x-coordinate of the vertex of the parabola with that equation is
 .
The y-coordinate of the vertex is
 .
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