I can't solve the last exercises in a worksheet of Pre-Calculus problems. It says:
Quadratic function $f(x)=ax^2+bx+c$ determines a parabola that passes through points $(0, 2)$ and $(4, 2)$, and its vertex has coordinates $(x_v, 0)$.
a) Calculate coordinate $x_v$ of parabola's vertex.
b) Calculate $a, b$ and $c$ coefficients.
How can I get parabola's equation with this information and find what is requested?
I would appreciate any help. Thanks in advance.