**Determine the quadratic function f whose vertex is (1,-1) and passes through (2,1). Type answer in form f(x)=ax^2+bx+c**

**Answer:**

We know that the vertex is (1,-1),

then the function can be written as:

f(x) = a(x-1)^2 -1

=a(x^2 - 2x +1) -1

= ax^2 - 2ax + (a-1)

then: a = a

b = -2a

c = a-1

Now let’s find a :

f(2) = a*2^2 + 2*b +c = 1

1 = 4a + 2b +c

1 = 4a + 2(-2a) + a-1

1 = 4a-4a+a-1

a = 2

then b = -2a = -4

c = a-1 = 1

So the function is : f(x) = 2x^2 -4x +1