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Slopes of curves w/o equation?

by donlin
Tags: curves, equation, slopes, w or o
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donlin
#1
Sep18-06, 12:45 PM
P: 3
I have three points on a Y= -ax^2 + bx + c graph (negative parabola). I don't know how to find the equation with this information. Tangent lines? Help.
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neutrino
#2
Sep18-06, 12:51 PM
P: 2,047
Hi donlin. Welcome to PF!
Let's say one of the points is (x0, y0). What's -ax02+bx0+c equal to?
radou
#3
Sep18-06, 12:54 PM
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Your equation is a function of one variable, Y(x)=-ax^2+bx+c. If a point (x0, y0) lies on the parabola, it must satisfy the equation f(x0) = y0. Since you have three points, after 'plugging' every one of them into the equation, you'll have three equations with three unknowns a, b and c, which are the coefficients you need.

donlin
#4
Sep18-06, 01:15 PM
P: 3
Slopes of curves w/o equation?

I think I have the slope, by connecting point A to B and then rise over run, but I don't know how to get the rest of the equation. Basically, I have a point A and slope, but I don't have the coefficients or y-intercept.
donlin
#5
Sep18-06, 01:16 PM
P: 3
Quote Quote by neutrino
Hi donlin. Welcome to PF!
Let's say one of the points is (x0, y0). What's -ax02+bx0+c equal to?
I think it's equal to y0.
neutrino
#6
Sep18-06, 01:31 PM
P: 2,047
Quote Quote by donlin
I think I have the slope, by connecting point A to B and then rise over run, but I don't know how to get the rest of the equation. Basically, I have a point A and slope, but I don't have the coefficients or y-intercept.
You can't get the slope at one point of a parabola by connecting two points on it. It's different at every point. Use the method that radou posted.
HallsofIvy
#7
Sep18-06, 02:46 PM
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Quote Quote by donlin
I think I have the slope, by connecting point A to B and then rise over run, but I don't know how to get the rest of the equation. Basically, I have a point A and slope, but I don't have the coefficients or y-intercept.
A curve does not have a slope! What you have found is the slope of the line through A and B which is irrelevant. If your question is how to find the equation of a parabola passing through three points, just put the x and y coordinates of each point into your general equation, Y= -ax^2 + bx + c, gives you three linear equations for A, B, and C.


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