The derivative function y'=2ax+b is the tangent slope of any point (x, y) on the image of quadratic function y = ax 2+bx+c (the geometric meaning of derivative function).

The tangent slope of a point (x0, y0) on the image of quadratic function y = ax 2+bx+c is 2ax0+b.

Therefore, from an oblique point of view, the same is true.

Y-y0=(2ax0+b)(x-x0) is the tangent analytic formula.