Determine the equation of a parabola with roots $2 + \sqrt {3}$ and $2 - \sqrt {3}$, and passing through the point $(2,5)$

Question

My attempt:

$$f(x) = a(x - r)(x - s)$$ $$f(x) = a(x-(2 + \sqrt {3}))(x-(2- \sqrt {3}))$$

From here, I'm stuck. I can't remember where to go from this point and need some help.

Answer 1

You've used several pieces of your information, but not all. You haven't used the fact that it passes through $(2,5)$, i.e. that $f(2) = 5$. So you should plug in $2$ and $5$ and then solve for $a$.