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No, there are an infinity of parabolas that can be draw through three points, each one with a different axial direction. Of course, il you asume a given direction for the axis, the parabola is unique.if you assume it's a parabola then such a parabola is unique
There are infinitely many curves you can draw through three points. The simplest method it to use a 2nd order polynomial (i.e a parabola). Just write out 3 equations using the values of x & y:
y1 = a x21 + b x1+ c
y2 = a x22 + b x2+ c
y3 = a x23 + b x3+ c
This is 3 equations in 3 unknowns (a,b,c) that can be solved by substitution.
optics.tech said:What about if the amount of the points are nine pieces?
Will above equations can be continued from three to nine equations with similar pattern?
Does this curve is a kind of smooth and continue curve?
To plot a curve with given three points, you can use the slope-intercept form of a line equation, y=mx+b, where m is the slope and b is the y-intercept. First, find the slope using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two of the given points. Then, substitute the slope and one of the points into the equation to find the value of b. Finally, use the equation to plot the curve on a graph.
Yes, you can plot a curve with three points that are not collinear. However, keep in mind that the curve may not be a straight line, since three non-collinear points can form a unique curve.
No, it is not necessary to use the slope-intercept form of a line equation. Other forms of equations, such as point-slope form or standard form, can also be used to plot a curve with three points. However, the slope-intercept form is usually the most straightforward and commonly used method.
If one of the given points is an outlier, it may significantly affect the curve's shape and equation. In this case, it may be more accurate to plot the curve with the remaining two points and adjust the equation accordingly. Alternatively, you can use statistical methods, such as regression analysis, to determine the best-fit curve for the given points.
Yes, there are limitations to plotting a curve with three points. The curve may not accurately represent the data if the points are not evenly spaced or do not follow a specific pattern. Additionally, using only three points may not provide enough information to determine the exact shape of the curve, especially if the points are relatively close to each other.