
Quadratic Equation
I have a test in a few hours and this problem is on my review sheet and I am having trouble with it. If someone can help me out I would really appreciate it!!!!!!!!1
Find the equation of the quadratic function that has the given vertex and given point
V (4,3) through (5,2)

Let $\displaystyle f(x)=ax^2+bx+c$
Then,
$\displaystyle \left\{\begin{array}{lll}\frac{b}{2a}=4\\\frac{\Delta}{4a}=3\\ f(5)=2\end{array}\right.\Rightarrow\left\{\begin{array} {lll}b=8a\\b^24ac=12a\\25a5b+c=2\end{array}\right.$
Now solve the system.