Register to reply

Slopes of curves w/o equation?

by donlin
Tags: curves, equation, slopes, w or o
Share this thread:
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.
Phys.Org News Partner Science news on Phys.org
Physical constant is constant even in strong gravitational fields
Montreal VR headset team turns to crowdfunding for Totem
Researchers study vital 'on/off switches' that control when bacteria turn deadly
neutrino
#2
Sep18-06, 12:51 PM
P: 2,046
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
HW Helper
radou's Avatar
P: 3,220
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: 2,046
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
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,691
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.


Register to reply

Related Discussions
Equation for how much an object curves space-time Astronomy & Astrophysics 3
Find a function F(x,y) whose level curves are solutions to the differential equation Calculus & Beyond Homework 7
Trouble understanding slopes General Math 1
Slopes homework Introductory Physics Homework 0
Learning about finding the slope of a line General Math 35