Determining the equation of the quadratic function with the points (-1,4), (1, -2) and (2,1)?

We'll write the equation of the
parabola:

y = ax^2 + bx + c

Since the
parabola is passing through the points (-1,4), (1, -2) and (2,1), we'll
have:

f(-1) = 4

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

a(-1)^2 + b(-1) + c =
4

a - b + c = 4 (1)

f(1) =
-2

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

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

a + b
+ c = -2 (2)

f(2) = 1

We'll substitute
x by 2 in the expression of quadratic:

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

4a + 2b + c = 1 (3)

We'll add (1) +
(2):

a - b + c + a + b + c = 4 -2

We'll
combine and eliminate like terms:

2a + 2c =
2

We'll divide by 2:

a + c = 1
(4)

We'll add (3) + 2*(1):

4a + 2b + c
+ 2a - 2b + 2c = 8 + 1

We'll combine and eliminate like
terms:

6a + 3c = 9

We'll divide by
3:

2a + c = 3 (5)

We'll subtract (4)
from (5):

2a + c - a - c = 3 - 1

We'll
combine and eliminate like terms:

a =
2

4 + c = 3

c = 3 -
4

c = -1

a
- b + c = 4

2 - b - 1 = 4

-b = 4 - 2 +
1

b =
-3

The quadratic equation
is:

y = 2x^2 - 3x -
1