Final answer:
The quadratic function that passes through the points (0, -2), (1, 0), and (2, 4) is f(x) = 2x^2 - 2.
Step-by-step explanation:
The quadratic function that passes through the points (0, -2), (1, 0), and (2, 4) can be determined by substituting these points into the general quadratic function equation y = ax^2 + bx + c. Let's substitute each point into the equation and solve for a, b, and c.
Substitute point (0, -2):
-2 = a(0)^2 + b(0) + c
-2 = c
Substitute point (1, 0):
0 = a(1)^2 + b(1) + c
a + b + c = 0
Substitute point (2, 4):
4 = a(2)^2 + b(2) + c
4 = 4a + 2b + c
Solving the system of equations:
From the first substitution, we have c = -2.
Substituting c = -2 into the second equation gives a + b - 2 = 0.
Substituting c = -2 into the third equation gives 4 = 4a + 2b - 2.
Simplifying these equations, we find a = 2, and b = 0.
Therefore, the quadratic function is f(x) = 2x^2 - 2.