Determine the quadratic function if the graph passes through the point (0;1) , (1;3) and (-1;1)

A quadratic function is described by the
expression:

f(x)=ax^2 + bx +
c

To determine the quadratic function, we'll have to
calculate the coefficients a, b, c.

We'll calculate the
coefficients using the condition given by enunciation: If the graph of the quadratic
passes through the given points, we'll have the
relations:

The point (0,1) is on the graph if and only
if:

f(0)=1

We'll substitute 0
in the expression of the quadratic:

f(0)=a*(0)^2 + b*(0) +
c=c

c=1

The point (1,3) is on
the graph if and only
if:

f(1)=3

We'll substitute 1
in the expression of the quadratic:

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

a+b+c=3, but
c=1

a+b+1=3

a+b=2

The
point (-1,1) is on the graph if and only
if:

f(-1)=1

We'll
substitute -1 in the expression of the
quadratic:

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

a-b+c=1

We  have also
the expression a-b+c=1 and
c=1

a-b+1=1

a-b=0

a=b,
but
a+b=2=>a+a=2

2a=2

a=1

b=1

c=1

The
expression of the quadratic
is:

f(x) = x^2 + x +
1