Asap 25 pts + brainliest to right/best answer

 y = -4x^2 + 4x - 3 which is choice A

Explanation:

We'll use the template y = ax^2 + bx + c to help find the equation

Plug in x = 0 and y =-3 which is from the point (0,-3)

y = ax^2 + bx + c

-3 = a(0)^2 + b(0) + c

c = -3

Plug in x = -1, y = -11 which is from the point (-1,-11). Also plug in c = -3

y = ax^2 + bx + c

-11 = a(-1)^2 + b(-1) + (-3)

-11 = a - b - 3

a-b = -11+3

a-b = -8

a = b-8 <<-- we'll use this later

Plug in x = 3, y = -27 which is from the point (3,-27). Also plug in c = -3

y = ax^2 + bx + c

-27 = a(3)^2 + b(3) + (-3)

-27 = 9a + 3b - 3

9a + 3b = -27+3

9a + 3b = -24

9(b-8) + 3b = -24 ... replace a with b-8 (works because a = b-8)

9b-72 + 3b = -24

12b-72 = -24

12b = -24+72

12b = 48

b = 48/12

b = 4

Use this b value to find 'a'

a = b-8

a = 4-8

a = -4

So we have

a = -4, b = 4, c = -3

This leads to the equation y = -4x^2 + 4x - 3 which is choice A

You can check the answer by plugging each point into the equation. You should get a true statement each time.

Example: plug in (0,-3)

y = -4x^2 + 4x - 3

-3 = -4(0)^2 + 4(0) - 3

-3 = -3

I'll let you check the others.

none cuz there are no "following statements" regarding the question

step-by-step explanation: