how to transform a parabola to a certain sense?
say I had 3 points on x,y
(0,0)
(4.67,7.83)
(28,0)
I have 18 other examples to graph and deviate, however could somebody tell me how to get a parabola to my liking -step by step- as I've lost some of my pre-cal knowledge.
Comments
Start with the equation
.. a*x^2 + b*x + c = y
Put in your x and y values, and you will get three linear equations in the unknowns a, b, c. These can be solved by the method of your choice. (Cramer's method works well.)
Your numbers here give
.. c=0, 21.8089 a + 4.67 b + c = 7.83, 784 a + 28 b + c = 0
which has solution
.. a = -0.0718671, b = 2.01228, c = 0.
This particular example can almost be done by inspection, as you know factors are x(x-28), and a scale factor will make this go through the point (4.67, 7.83). The scale factor will be
.. 7.83/(4.67*(4.67-28)) = -7.83/100.9511 ≈ -0.0718671
So the equation for this parabola is
.. y = -0.0718671x(x-28)