Calculating the Parabola Angle ```Name: Tom Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: How do you find an angle of a parabola if you only know the vertex and the ending point? Replies: This is a very easy problem for differential calculus. It can be solved geometrically, but that is more involved. Without derivation, here is the answer. The formula for a parabola is: y = kX^2. The slope of the tangent is given by: lim(d--->0) [Y(X + d) - Y(X)] / (X + d) - X = lim(d--->0) [k*(X +d)^2 - k*X^2] / (X + d) - X lim(d--->0) [k*(X^2 +2dX +d^2) - k*X^2 / (X + d) - X lim(d--->0 [2dX + d^2] / d neglecting terms quadratic in d, i.e. d^2 this is: lim(d--->0) [2dX] / d = 2 * X. So the slope, i.e. the tangent at any point X is simply 2*X Knowing that the tangent of the angle is 2*X, you can determine the angle as the inverse tangent. This you can do on a calculator or look it up in a trig table. This same process is used to determine the slope (i.e. the tangent) of any function. That is what differential calculus is all about. Vince Calder Click here to return to the Mathematics Archives

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