Question

what is the equation of the quadratic function that passes through the points (0,-1),(1,0),and (2,-3)

Answer 1

-2x^2 + 3x -1

Explanation:

y = ax^2 + bx + c

(0,-1):

-1 = a(0)^2 + b(0) + c

-1 = 0 + 0 + c

-1 = c

(1,0):

0 = a(1)^2 + b(1) + c

0 = a + b + c

(2,-3):

-3 = a(2)^2 + b(2) + c

-3 = 4a + 2b + c

Replace c with -1

0 = a + b -1

1 = a + b

-3 = 4a + 2b -1

-2 = 4a + 2b

-1 = 2a + b

Solve:

2a + b = -1

-1a - b = -1

a = -2

2a + b = -1

-2a -2b = -2

-b = -3 divide both by -1: b = 3

a = -2; b = 3; c = -1

y = ax^2 + bx + c or y = -2x^2 +3x -1