Question

Find values of A and B such that the graph of the given equation will contain the given points.

y = x² + Ax + B; (1,9), (-3,25)

Answer 1

The values of A and B for the quadratic equation y = x² + Ax + B that passes through (1,9) and (-3,25) are A = 2 and B = 6.

Step-by-step explanation:

To find values of A and B for the quadratic equation y = x² + Ax + B that goes through the points (1,9) and (-3,25), we can substitute these points into the equation and solve for A and B.

1. For the point (1, 9):
   9 = 1^2 + A(1) + B
   9 = 1 + A + B
2. For the point (-3, 25):
   25 = (-3)^2 + A(-3) + B
   25 = 9 - 3A + B

To find A and B, we need to solve these equations simultaneously.

1. From the first equation, we get:
   B = 9 - A - 1
   B = 8 - A
2. Substituting B into the second equation:
   25 = 9 - 3A + (8 - A)
   25 = 17 - 4A
   A = (17 - 25)/-4
   A = 2
3. Now, substituting A back into the equation for B:
   B = 8 - 2
   B = 6

Therefore, the values are A = 2 and B = 6.