Question

Determine the quadratic function of f whose vertex is (1,-4) and passes through (2,-1)
f(x)=?

Answer 1

let f(x)=ax^2+bx+c
the vertex is given by (-b/2a, f(-b/2a))
-b/2a = 1 ----------- 1
-4 = f(1) ----------- 2
-1 = f(2) ----------- 3
three equations three equations ... solve them to find the value of a,b,c

Answer 2

or plug them into wolfram to get direct solution
-b/2a = 1 ----------- 1
-4 = (1)^2a+(1)b+c ----------- 2
-1 = (2)^2a+(2)b+c ------------3