# Math Help - Slope of a curve at a point

1. ## Slope of a curve at a point

Find the equation of the tangent line to f(x)=X^2 that passes through the point (0, -4)

I only know how to find the equation of the tangent line AT a certain point

There are 2 possibilities I'm guessing but I'm not sure how to find them.

2. ## Re: Slope of a curve at a point

Let $(x, x^2)$ be the point of tangency. Then the slope of the line is $2x$. From the following picture you can find $x$.

3. ## Re: Slope of a curve at a point

Alternatively, use the point-slope formula for the line through (0, -4) with slope m.
y + 4 = m(x - 0)
Since y = x^2 and m = y' = 2x, we have
x^2 + 4 = 2x(x)
so 4 = x^2
x = +/-2...