Final answer:
The equation of the parabola with a vertex at (4, -2) and a y-intercept of 6 is y = 0.5(x - 4)^(2) - 2.
Step-by-step explanation:
The equation of a parabola with a vertex at (h, k) and a y-intercept of c is given by the equation y = a(x - h)^(2) + k. To find the equation of the parabola with a vertex at (4, -2) and a y-intercept of 6, we can substitute the values into the equation. Since the y-intercept occurs when x = 0, we can substitute x = 0 and y = 6 into the equation:
6 = a(0 - 4)^(2) + (-2)
6 = 16a - 2
16a = 8
a = 0.5
Therefore, the equation of the parabola is y = 0.5(x - 4)^(2) - 2.