SOLUTION: Can someone please help me with this problem: Determine whether the graph of each parabola opens upward or downward. g(x)=x^+x-6 Came up with this so far: x=-b/a x=-1/

Algebra ->  Algebra  -> Graphs -> SOLUTION: Can someone please help me with this problem: Determine whether the graph of each parabola opens upward or downward. g(x)=x^+x-6 Came up with this so far: x=-b/a x=-1/      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 29915: Can someone please help me with this problem:
Determine whether the graph of each parabola opens upward or downward.
g(x)=x^+x-6

Came up with this so far:
x=-b/a x=-1/2
now I am stuck...where do I go from here?
Any help would be greatly appreciated. Thank you in advance.

Answer by Earlsdon(6098) About Me  (Show Source):
You can put this solution on YOUR website!
Determine whether the graph of the parabola opens upward or downward.
g%28x%29+=+x%5E2%2Bx-6
If the coefficient of the x%5E2term is positive, the parabola opens upward, if it is negative, then it opens downward.
In this case, the coefficient is +1 so the parabola opens upward.
If you want to find the location of the vertex of the parabola, then you can use the fact that the x-coordinate of the vertex is given by:
x+=+-b%2F2a a = 1 and b = 1, so:
x+=+-1%2F2 now substitute this value of x into the original equation and solve for g(x).
g%28x%29+=+%28-1%2F2%29%5E2%2B%28-1%2F2%29-6
g%28x%29+=+%281%2F4%29-%281%2F2%29-6
g%28x%29+=+-6.25
The vertex is located at:(-0.5, -6.25)
Here's the graph:
graph%28300%2C200%2C-5%2C5%2C-8%2C4%2Cx%5E2%2Bx-6%29