jmc

Question

Let t be a parameter that varies over all real numbers. Any parabola of the form y = 3x^2 + tx - 2tpasses through a fixed point. Find this fixed point.

Accepted Answer

To obtain the fixed point, we want to eliminate t in the equation y = 3x^2 + tx - 2t.We can do so by taking x = 2. This leaves us with y = 3 2^2 = 12, so the fixed point is (2,12).