Question

Find a quadratic function that includes the set of values below.

(0,4) (2,10) (3,7)"
A. f(x) = 2x^2 - 5x + 4
B. f(x) = -x^2 + 3x + 4
C. f(x) = x^2 - 3x + 4
D. f(x) = -2x^2 + 5x + 4

Answer 1

To find a quadratic function that includes the given set of values, substitute the coordinates into the general form of a quadratic function and solve for the unknowns. The correct answer is option C: f(x) = x^2 - 3x + 4.

Step-by-step explanation:

To find a quadratic function that includes the given set of values, we can use the general form of a quadratic function: f(x) = ax^2 + bx + c. We can substitute the coordinates of the given points into this equation and solve for the values of a, b, and c.

1. Substituting the coordinates (0,4): 4 = a(0)^2 + b(0) + c → c = 4
2. Substituting the coordinates (2,10): 10 = a(2)^2 + b(2) + c → 4a + 2b + 4 = 10
3. Substituting the coordinates (3,7): 7 = a(3)^2 + b(3) + c → 9a + 3b + 4 = 7

Simplifying the equations, we get: c = 4, 4a + 2b = 6, and 9a + 3b = 3. Solving these equations simultaneously, we find a = 1, b = -3, and c = 4. Therefore, the quadratic function that includes the given set of values is f(x) = x^2 - 3x + 4, which corresponds to option C.