document.write( "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! \n" ); document.write( "

Algebra.Com's Answer #574933 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The graph of a parabola looks like this $\"graph%28100%2C100%2C.1%2C.5%2C-.5%2C-.1%2C-7%2A%28x-.3%29%5E2-.15%29\"$ or like this $\"graph%28100%2C100%2C.1%2C.5%2C.1%2C.5%2C7%2A%28x-0.3%29%5E2%2B.15%29\"$ .
\n" ); document.write( "First, solve for $\"y\"$ :
\n" ); document.write( " $\"x%5E2+%2B3y=0\"$ <--> $\"3y=-x%5E2\"$ <--> $\"y=-%281%2F3%29%2Ax%5E2\"$
\n" ); document.write( "That lat equation allows you to calculate points easily:
\n" ); document.write( "you pick a value for $\"x%5D%7D%7D%2C+plug+it+in%2C+and+calculate+%7B%7B%7By\"$
\n" ); document.write( "(for example, for $\"x=3\"$ , $\"y=-%281%2F3%29%2A3%5E2=-%281%2F3%29%2A9=-3\"$ ).
\n" ); document.write( "Looking at that equation, you realize that:
\n" ); document.write( "for $\"x=0\"$ , $\"y=-%281%2F3%29%2A0=0\"$ , and
\n" ); document.write( "for $\"x%3C%3E0\"$ (negative or positive), $\"x%5E2%3E0\"$ and $\"y=-%281%2F3%29%2Ax%5E2%3C0\"$ .
\n" ); document.write( "That tells you that the graph looks like this:
\n" ); document.write( " $\"graph%28300%2C200%2C-3%2C3%2C-2%2C2%2C-x%5E2%2F3%29\"$ It has a maximum at $\"O%280%2C0%29\"$ , the origin,
\n" ); document.write( "and all the other points are below the x-axis, with $\"y%3C0\"$ .
\n" ); document.write( "In general a parabola with vertex at $\"V%28h%2Ck%29\"$ has an equation of the form
\n" ); document.write( " $\"y=a%2A%28x-h%29%5E2%2Bk\"$ <---> $\"y=a%28x%5E2-2hx%2Bh%5E2%29%2Bk\"$ <---> $\"y=ax%5E2-2ahx%2Bah%5E2%2Bk\"$ .
\n" ); document.write( "You may be told that it is a quadratic function of the form $\"y=ax%5E2%2Bbx%2Bc\"$ ,
\n" ); document.write( "but that is the same thing,
\n" ); document.write( "with $\"b=-2ah\"$ and $\"c=ah%5E2%2Bk\"$ .
\n" ); document.write( "In any case, you can find $\"h\"$ , the x-coordinate of the vertex,
\n" ); document.write( "by changing the sign of the coefficient of the term in $\"x\"$ ,
\n" ); document.write( "to get $\"-b=2ah\"$ ,
\n" ); document.write( "and dividing by $\"2a\"$ , twice the coefficient of the term in $\"x%5E2\"$ ,
\n" ); document.write( "to get $\"h=-b%2F2a=2ah%2F2a\"$ .
\n" ); document.write( "After that, you just plug that value of $\"x\"$ into the equation and find $\"k\"$ ,
\n" ); document.write( "the y-coordinate of the vertex.
\n" ); document.write( "For example,
\n" ); document.write( " $\"y=4x%5E2%2B6x%2B8\"$ has $\"a=4\"$ and $\"b=6\"$ .
\n" ); document.write( "The x-coordinate of the vertex of the parabola with that equation is
\n" ); document.write( " $\"h=-6%2F4=-3%2F2=-1.5\"$ .
\n" ); document.write( "The y-coordinate of the vertex is
\n" ); document.write( " $\"x=4%2A%28-1.5%29%5E2%2B6%2A%28-1.5%29%2B8=4%2A2.25-9%2B8=9-9%2B8=8\"$ . \n" ); document.write( "

\n" );