The maximum point of a quadratic curve is $(-2,-5)$. The curve cuts the $y$-axis at $-13$. Find the equation of the curve. Give your answer in the form $y = ax^2+bx+c$.
For this question I learnt I had to use the standard form $f(x)=a(x−h)^2+k$ first. Then the general form $f(x)=ax^2+bx+c$ of the equation of a curve.
What does the 'a' part of standard form equation of a curve represent. I understand that the '(x−h)2+k' is a sort of reversal of the result of when you use the completing the square to find the turning point of the curve but what does the 'a' part represent.
I have completed the question, I am just curious. I have only finished GCSE so if the answer could be "dummed" down that would be appreciated