SOLUTION: The vertex of a parabola is at the point (3, 2.5) and the point (4, 5.5) is on the parabola. What is the equation of the parabola? ... i know that the formula for parabola that

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> SOLUTION: The vertex of a parabola is at the point (3, 2.5) and the point (4, 5.5) is on the parabola. What is the equation of the parabola? ... i know that the formula for parabola that      Log On

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Question 144632: The vertex of a parabola is at the point (3, 2.5) and the point (4, 5.5) is on the parabola. What is the equation of the parabola?
... i know that the formula for parabola that is up or down is
y=a(x-h)exponent 2+v ... what im having truble finding is (a).
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
For our vertex, the equation's formula is:
%28x-3%29%5E2=4p%28y-2.5%29
(4, 5.5) is on the parabola. Put these values in our formula to find p.
1%5E2=4p%283%29
Thus p=1%2F12
And our equation becomes
%28x-3%29%5E2=%281%2F3%29%28y-2.5%29
3%28x-3%29%5E2%2B2.5=y
Another way to think about this is that the non-vertex point you are given is only 1 unit over to the right and it goes up 3 units from the vertex, so your "a" value would logically be 3 (1 increase of x results in 3 increase in y).
I edited this because I made it more complicated than it needed to be prior to this current revision. Good day
graph%28+300%2C+300%2C+-2%2C+6%2C+-2%2C+6%2C+3%28x-3%29%5E2%2B2.5%29