Question

Fit a quadratic function to these three points:


(−1, −11), (0, −3), and (3, −27)




y = −4x2 − 4x − 3



y = −4x2 + 4x − 3



y = −4x2 − 4x + 3



y = 4x2 − 4x − 3

Answer 1

Answer:

$\large\boxed{y=-4x^2+4x-3}$

Step-by-step explanation:

$y=-4x^2-4x-3\\\\\text{Check for}\ (-1,\ -11):\\\\-11=-4(-1)^2-4(-1)-3\\-11=-4(1)+4-3\\-11=-4+4-3\\-11=-3\qquad\boxed{FALSE}\\===========================\\y=-4x^2+4x-3\\\\\text{Check for}\ (-1,\ -11):\\\\-11=-4(1)^2-4(1)-3\\-11=-4-4-3\\-11=-11\qquad\boxed{CORRECT}\\\\\text{Check for}\ (0,\ -3):\\\\-3=-4(0)^2+4(0)-3\\-3=-3\qquad\boxed{CORRECT}\\\\\text{Check for}\ (3,\ -27):\\\\-27=-4(3)^2+4(3)-3\\-27=-4(9)+12-3\\-27=-36+12-3\\-27=-27\qquad\boxed{CORRECT}$

$===========================\\y=-4x^2-4x+3\\\\\text{Check for}\ (-1,\ -11):\\\\-11=-4(-1)^2-4(-1)+3\\-11=-4(1)+4+3\\-11=-4+4+3\\-11=3\qquad\boxed{FALSE}\\===========================\\y=4x^2-4x-3\\\\\text{Check for}\ (-1,\ -11):\\\\-11=4(-1)^2-4(-1)-3\\-11=4(1)+4-3\\-11=4+4-3\\-11=5\qquad\boxed{FALSE}$