Question

Write the quadratic function that goes through the points: (0,1), (2, -7), and (-1,11).

a) f(x) = -3x^2 + 2x + 1
b) f(x) = 3x^2 - 4x + 1
c) f(x) = -3x^2 - 4x + 1
d) f(x) = 3x^2 + 4x + 1

Answer 1

To write the quadratic function that goes through the given points, substitute the x and y values into the general form of a quadratic function and solve for the coefficients. The correct quadratic function is f(x) = -3x^2 + 2x + 1.

Step-by-step explanation:

To write the quadratic function that goes through the points (0,1), (2,-7), and (-1,11), we can use the general form of a quadratic function: f(x) = ax^2 + bx + c. By substituting the x and y values of the given points into the function, we can form three equations to solve for the coefficients a, b, and c. Solving these equations, we find that the correct quadratic function is f(x) = -3x^2 + 2x + 1. Therefore, the correct answer is option a) f(x) = -3x^2 + 2x + 1.

Answer 2

To write the quadratic function that goes through the given points, substitute the x and y values into the general form of a quadratic function and solve for the coefficients. The correct quadratic function is f(x) = -3x^2 + 2x + 1.

Step-by-step explanation:

To write the quadratic function that goes through the points (0,1), (2,-7), and (-1,11), we can use the general form of a quadratic function: f(x) = ax^2 + bx + c. By substituting the x and y values of the given points into the function, we can form three equations to solve for the coefficients a, b, and c. Solving these equations, we find that the correct quadratic function is f(x) = -3x^2 + 2x + 1. Therefore, the correct answer is option a) f(x) = -3x^2 + 2x + 1.