Math
posted by momo on .
How do I create a quadratic equation that passes through the points (1,2),(1,7),(4,5)?

y = a x ^ 2 + b x + c
In this case:
For x =  1 , y = 2
2 = a (  1 ) ^ 2 + b (  1 ) + c
a  b + c = 2
For x = 1 , y = 7
7 = a ( 1 ) ^ 2 + b 1 + c
a + b + c = 7
For x = 4 , y = 5
5 = a ( 4 ) ^ 2 + b 4 + c
16 a + 4 b + c = 5
So you must solve system of 3 equations :
a  b + c = 2
a + b + c = 7
16 a + 4 b + c = 5
The exact solutions are :
a =  19 / 30
b = 5 / 2
and
c = 77 / 15
y = (  19 / 30 ) x ^ 2 + ( 5 / 2 )x + 77 / 15