Find the quadratic whose graph is passing through the points (-1,3), (0,-1), (2,4)

We'll write the general form of the
quadratic:

ax^2 + bx + c =
y

If the graph passes through the given points, that means
that the coordinates of the points verify the equation of the
quadratic.

The point A(-1,3) belongs to the graph if and
only if

yA = axA^2 + bxA +
c

We'll substitute the coordinates of the point A into the
equation:

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

a - b + c = 3 (1)

The point
B(0,-1) belongs to the graph if and only if

yB = axB^2 +
bxB + c

We'll substitute the coordinates of the
point B into the equation:

c =-
1

The point C(2,4) belongs to the graph if
and only if

yA = axC^2 + bxC +
c

We'll substitute the coordinates of the point C into the
equation:

4 = 4a + 2b -
1

We'll add 1 boh sides:

4a +
2b = 5 (2)

We'll substitute the value of c in
(1):

a - b -1 = 3 (1)

We'll
add 1 both sides:

a - b = 4
(3)

We'll multiply (3) by
2:

2a - 2b = 8 (4)

We'll add
(4)+(2):

4a + 2b + 2a - 2b =
5+8

6a = 13

We'll divide by
6:

a =
13/6

We'll substitute a in
(3):

13/6 - b = 4

We'll
subtract 13/6 both sides:

-b = 4 -
13/6

-b = 11/6

b
= -11/6

The quadratic
is:

f(x) = (13/6)*x^2 - (11/6)*x -
1