How do I determine quadratic function f, whose graph is vertex (1,-2) and passes thru (3,6)

Question

anonymous · Answer

Let the quadratic function be of the genera form 

$$ f(x)=ax^2+bx+c$$
Then match the three unknown coefficients to the points

$$f(1)=-2 \ f(3)=6$$
And for the Vertex 

$$1 = \frac{-b}{2a} \rightarrow 2a=-b $$
Then solve system of equation

anonymous · Answer

ok, but how do I plug my numbers in

anonymous · Answer

$$f(1)=a+b+c=-2 \
f(3)=9a+3b+c = 6 \2a=-b $$

anonymous · Answer

System of equations, three unknowns, three equations, therefore one definite solution, because none of the equations above is redundant.

anonymous · Answer

i still don't understand

anonymous · Answer

Do you know how to solve a system of linear equations?