Question

Formulate the quadratic function that contains the points (-2,1), (0,1) and (1,4).

o f(x) = x2 + 2x +1
Of(x) = x2 - 2x + 1
Of(x) = x2 - 2x - 1
o f(x) = x2 + 2x - 1

Answer 1

Answer: A) f(x) = x² + 2x + 1

Explanation:

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) → 6 = 2A + 2B

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