How do I create a quadratic equation that passes through the points (-1,2),(1,7),(4,5)?

Answer 1

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