The question reads:
Find the values of m for which the line y = mx - 9 is a tangent to the curve x^2 = 4y.
All I need is the basic formula? I can't find one anywhere.
differentiate both sides
$\displaystyle \frac{d}{dx}(x^2)=\frac{d}{dx}(4y)$
$\displaystyle 2x=4\frac{dy}{dx}$
$\displaystyle \frac{dy}{dx}=\frac{1}{2}x$
now $\displaystyle \frac{dy}{dx}$ would be the gradient of the curve (m in the formula)
substitute this in along with $\displaystyle y=\frac{1}{4}x^2$ (you are given this) into the equation of the line you want to find and solve this for x
I get
$\displaystyle x=\pm6$
now plug these values into your expression for $\displaystyle \frac{dy}{dx}$ to find the values of m (remember dy/dx=m)