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

quadratic-function

#1

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) = a2^2 + 2b +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