Question 15590: How do you find the quadratic equation of a parabola with a vertex of (8, 102), a y-intercept of (0, 98.6) and a zero of (16,0)? I have tried to solve the equation -(b/2a) =8, but that hasn't worked out well. I've also tried to solve for a or b since I know that c is equal to 98.6, but so far I cannot get the right equation. All I have is that 64a + 8b + 98.6 = 102 and 256a + 16b + 98.6 = 0. I know a is a negative number, but that is the only other information I have.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! (8, 102), a y-intercept of (0, 98.6) and a zero of (16,0)? I have tried to solve the equation -(b/2a) =8, but that hasn't worked out well. I've also tried to solve for a or b since I know that c is equal to 98.6, but so far I cannot get the right equation. All I have is that 64a + 8b + 98.6 = 102 and 256a + 16b + 98.6 = 0.
I think that you started from 
that is a long way for this question.
Try to start up with 
(same meaning as -b/2a =8 but easier)
and use point (16,0) to get -102 = 64 a
then we have a = - 51/32 and the equation of the parabola.
to get check if (0,98.6) [a very uugly number] is on the curve or not.
If not the question is wrong. (I guess so) and so no solution.
What happened ???
Because (8,102) cannot be the vertex, the question with wrong given
condition.
Normally, if we know the vertex then one more point is enough to
determine the parabolic function.
So, unfortunately, I guess you have to solve
this two ugly equations:
64a + 8b + 98.6 = 102 ...(1)
256a + 16b + 98.6 = 0....(2)
By (2)-(1)*2: ..... a = ??? then b =???
to find a & b.
And the final solution means (8,102) is just a point on the parabola
but not the vertex.
Good luck!
Kenny
PS: I think you can understand what I mean.
Normally, I don't answer such kinds of simple questions.
Since, you showed your work, I am gald to guide you some short cut.
|
|
|
