Question

Write an equation of a parabola that passes through the points (-3,-4),(-2,-5) and (1,4)

Answer 1

Answer:

y = x² + 4x - 1

Step-by-step explanation:

y = Ax² + Bx + C

-4 = A(-3)² + B(-3) + C = 9A - 3B + C

-5 = A(-2)² + B(-2) + C = 4A -2B + C

subtract these              

1 = 5A - B

B = 5A - 1

4 = A(1)² + B(1) + C = A + B + C

C = 4 - A - B

C = 4 - A - 5A + 1

C = 5 - 6A

-4 = 9A - 3B + C

-4 = 9A - 3(5A - 1) + 5 - 6A

-4 = 9A - 15A + 3 + 5 - 6A

-12 = -12A

A = 1

B = 5(1) - 1 = 4

C = 5 - 6(1) = -1

y = x² + 4x - 1