How do you find the equation for a curve between two points?

Question

The curve I have is a quadratic that passes through the points #x=-3#, #x=2#, and #y=-3#. I need to find the equation of the curve between #x=-3# and #x=2#.

Evelyn Agard · Accepted Answer

Information provided is insufficient for finding equation of the curve. There could be innumerable curves between the given lines.

There could be innumerable curves (though there would be only one line) between two points. You need to find the equation of the curve between #x=−3#, #x=2# and #y=-3#. These do not even indicate points but three lines and hence information provided is insufficient for finding equation of the curve. .

Isaiah Allen · Answer

undefined To find the equation for a curve between two points, you can follow these general steps:

1. Determine the coordinates of the two points, let's call them $ (x_1, y_1) $ and $ (x_2, y_2) $.
2. Write down the general equation for the type of curve you're dealing with. For example, if it's a straight line, use the equation $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.
3. Use the coordinates of the points to set up a system of equations.
4. Solve the system of equations to find the values of the parameters in the equation.
5. Write down the equation of the curve using the values of the parameters obtained.

If you're dealing with a specific type of curve, such as a polynomial or trigonometric function, the process might vary slightly, but the basic idea remains the same: use the given points to find the coefficients or parameters of the equation that fits the curve between those points.