A parabolla passes through the points (1,0), (2,2), (3,10). Deterine its equation.

A point is on a graph if it's coordinates verify the
equation of the graph.

We'll use this rule to determine the
equationof the parabola.

We'll write the standard equation
of a parabola:

y = ax^2 +bx +
c

Since (1,0) is on the parabola, we'll
have:

0 = a + b + c

We'll use
symmetric property and we'll get:

a + b + c = 0
(1)

Since (2,2) is on the parabola, we'll
have:

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

Since (3,10) is on the parabola, we'll
have:

9a + 3b + c = 10
(3)

We'll subtract (1) from (2) and we'll
get:

4a + 2b + c - a - b - c =
2-0

We'll combine like
terms:

3a + b = 2 (4)

We'll
subtract (1) from (3) and we'll get:

9a + 3b + c - a - b -
c = 10 - 0

We'll combine like
terms:

8a + 2b = 10 (5)

We'll
multiply (4) by -2:

-6a - 2b = -4
(6)

We'll add (6) to (5):

8a +
2b - 6a - 2b = 10 - 4

We'll combine and eliminate like
terms:

2a = 6

We'll divide by
2:

a =
3

We'll substitute a in
(4):

9 + b = 2 (4)

We'll
subtract 9 both sideS:

b = 2 -
9

b =
-7

We'll substitute a and b in
(1):

a + b + c = 0

3 - 7 + c =
0

-4 + c = 0

We'll add
4:

c =
4

The equation of the parabola
is:

y = 3x^2 - 7x +
4