quadratic functions?

Question

If you have a parabola on a graph and three of the points are...
(1, 19) (-1, 7) (-2, 13)
how can you find the quadratic equation, or function, for that graph?

Answer 1

Equation of a parabolic function:
y = ax^2 + bx + c

Plug in each of the points and solve the system:
19 = a + b + c
7 = a - b + c
13 = 4a - 2b + c

Subtracting the 2nd equation from the 1st:
12 = 2b
b = 6

Substitute back into 1st equation:
19 = a + (6) + c
13 = a + c
c = 13 - a

Substitute into 3rd equation:
13 = 4a - 2b + c
13 = 4a - 2(6) + (13 - a)
13 = 4a - 12 + 13 - a
12 = 3a
a = 4

Back to 1st equation:
19 = a + b + c
19 = (4) + (6) + c
19 = 10 + c
c = 9

So a=4, b=6, c=9

y = 4x^2 + 6x + 9

Answer 2

Assume that the quadratic is y = ax^2 + bx +c. You can then use the data to formulate equations, of which the first is 19 = a (1)^2 + b (1) + c. Construct the other two, and then solve the set as a linear system to get the values of the coefficients.

Answer 3

y=a*x^2+b*x+c,
enter all the points into the equation and you have this equation system.
a+b+c=19 ->this is from (1,19) consider this equation 1
a-b+c=7 -> this is from (-1,7) consider this equation 2
4a-2b+c=13 -> this is from (-2,13) consider this equation 3

Now eliminate a and c from equation 1 using equation 2
a + b + c =19
a - b + c = 7
--------------------- -
2b=12, so b=6

Now subtitute b=6 into equation 1
a+b+c = 19
a+6+c= 19
a+c=19-6
a+c= 13, consider this equation 4

Now subtitute b=6 into equation 3
4a-2b+c=13
4a-12+c=13
4a+c=13+12
4a+c= 25, consider this equation 5

Now eliminate c from equation 5 using equation 4
4a+c = 25
a + c = 13
--------------- -
3a = 12 , a =4

Because a=4 and b=6, then we use equation 1
a+b+c=19
4+6+c=19
10+c=19
c=19-10=9

so the quadratic equation is
y=4x^2+6x+9

Or, in computer langguage it is
y=4*x^2+6*x+9

Answer 4

General equation of parabola is:-
y = ax² + bx + c
19 = a + b + c
7 = a - b + c
13 = 4a - 2b + c

26 = 2a + 2c

38 = 2a + 2b + 2c
13 = 4a - 2b + c-------ADD

51 = 6a + 3c

51 = 6a + 3c
26 = 2a + 2c

51 = 6a + 3c
- 78 = - 6a - 6c-----ADD
- 27 = - 3c
c = 9

51 = 6a + 27
6a = 24
a = 4

13 = 16 - 2b + 9
2b = 12
b = 6

a = 4 , b = 6 , c = 9

Equation of parabola is:-
y = 4x² + 6x + 9

Answer 5

ya right like im going to solve that. do it on ur own u lazy piece of baloney