Answer: A) f(x) = x² + 2x + 1
<u>Step-by-step explanation:</u>
The standard form of a quadratic equation is: y = Ax² + Bx + C
Input (x, y) coordinates into the standard equation to solve for A, B, & C.
(0, 1) → 1 = A(0)² + B(0) + C
1 = C
(-2, 1) → 1 = A(-2)² + B(-2) + C
1 = 4A - 2B + 1
0 = 4A - 2B
(1, 4) → 4 = A(1)² + B(1) + C
4 = A + C + 1
3 = A + B
Solve the system of equations:
0 = 4A - 2B → 1(0 = 4A - 2B) → 0 = 4A - 2B
3 = A + B → 2(3 = A + B) → <u>6 = 2A + 2B</u>
6 = 6A
1 = A
Input A = 1 into either equation to solve for B:
3 = A + B
3 = 1 + B
2 = B
Now, Input A = 1, B = 2, and C = 1 into the standard equation:
y = (1)x² + (2)x + (1)
y = x² + 2x + 1