Question

Which quadratic regression equation models the following data points?

(1, 6), (3, 8), (7,0)
a. f(x) = -0.5x2 + 3x + 3.5
c. f(x) = 0.5x2 + 3x + 3.5
b. f(x) = -0.5(x − 3)(x – 3.5)
d. f(x) = -0.5(x + 3)(x +3.5)

Answer 1

The quadratic regression equation that models the given data points (1, 6), (3, 8), and (7,0) is f(x) = -0.5x^2 + 3x + 3.5, as all the data points fit this equation.

Step-by-step explanation:

To determine which quadratic regression equation models the given data points (1, 6), (3, 8), and (7,0), we start by testing each option provided:

1. f(x) = -0.5x2 + 3x + 3.5

   Testing the points:

   • f(1) = -0.5(1)2 + 3(1) + 3.5 = 6 ✓
   • f(3) = -0.5(3)2 + 3(3) + 3.5 = 8 ✓
   • f(7) = -0.5(7)2 + 3(7) + 3.5 = 0 ✓

2. We do not need to test the other options because all points fit with the first equation.

Therefore, the quadratic regression equation that models these data points is:

f(x) = -0.5x2 + 3x + 3.5