based on the example 2 in this website

 

why does the normal equation doesn't perpendicular to the tangent?

 

 

or i do any calculation wrong?

Vastor - your scales are confusing your eye.

 

Try thinking mathematically - if the slope of tangent is 4 - what must the slope of the normal be? Remember you can ignore the constants for the slope - just look at the coefficients of the x terms.

 

I used the graphing tool suggested and it produced a much more easily understood graph than yours - and because it held the scales the same it looked like a right angle too!

In more simple words: your problem is that the distance from 0 - 2 on the X-axis is not the same as the distance 0 - 2 on the Y-axis.