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donlin
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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.
neutrino said:Hi donlin. Welcome to PF!
Let's say one of the points is (x0, y0). What's -ax02+bx0+c equal to?
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.donlin said: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.donlin said: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.
The slope of a curve without an equation refers to the rate of change of that curve at a particular point. It can be determined by finding the tangent line to the curve at that point and calculating its slope.
To find the slope of a curve without an equation, you can use the slope formula: (change in y)/(change in x). This involves selecting two points on the curve and calculating the change in y and change in x between those points.
Yes, the slope of a curve without an equation can be determined graphically by drawing a tangent line to the curve at a specific point and calculating its slope. This can be done using a ruler or by using a computer program with graphing capabilities.
One limitation is that the accuracy of the slope will depend on the scale and precision of the graph. Another limitation is that it can be more time-consuming to find the slope graphically compared to using an equation.
Finding the slope of a curve without an equation is important because it allows us to understand the behavior of the curve at a specific point. It can also be used to analyze and make predictions about the curve's behavior in the future.