<s>[INST] How to find the equation of the tangent line to $y=x^2+2x-4$ at $x=2$? 
I'm given a curve $$y=x^2+2x-4$$
How do I find the tangent line to this curve at $x = 2$?

 [/INST] General formulas
$y=f(x)=x^2+2x-4$
$m=f'(x)=2x+2$  Slope equation
Point-Slope equation of a line
$(y-y_0)=m_0\cdot(x-x_0)$ 
Compute actual values
$x_0 = 2$
$y_0=f(x_0)=f(2)=(2)^2+2(2)-4=4+4-4=4$ 
$m_0=f'(x_0)=f'(2)=2(2)+2=4+2=6$
Substitute values into the line equation
$y-4=6\cdot(x-2)$
$y=6\cdot(x-2)+4$
$y=6x-8$
General Formula for a tangent line to a Parabola @ point $x_0$ on the Parabola
$y=f'(x_0)\cdot(x-x_0)+f(x_0)$
</s>