> Hello, can you please help me to resolve the > following? > > 1) If points Z1 and Z2 are known, what is the minimum > number of additional points we need to know in order > to define a parabola? > 2) What will be the formula to describe the parabola > using Y and X two-dimensional plane? > 3) What will be the formula to calculate value of M1 > and M2?
Dear kelvin m, >From your figure you are dealing with a parabola with an axis of symmetry parallel to the y-axis, so it will be of the form y=a.x^2 + b.x + c so you need 3 points to fully determine it, but they can't all be in a straight line otherwise the parabola will be degenerate. >From point Z1(0,4) we get c=4 >From point Z2(80,0) we get 0=a.80^2 + b.80 + 4 ...(1) Let's assume the third point is Z3(40,8) It doesn't have to have its x-value midway between Z1 and Z2, but from your figure its y-value should be greater than 5 for 0<x<80 Then Z3 gives 8=a.40^2 + b.40 + 4 ...(2) Solve (1) and (2) for a and b and we get y = -(3/800).x^2 +(1/4).x + 4 To get M1 and M2 find the y values of the parabola for the two given x values and compare to y=5 Regards, Peter Scales.