Final answer:
The equation of the parabola with a vertex at (4, -2) and a y-intercept at 6 is y = ½(x-4)^2 - 2.
Step-by-step explanation:
To write the equation of a parabola in vertex form given the vertex at (4, -2) and a y-intercept at 6, we start with the vertex form of a parabola's equation, which is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. For this equation, h=4 and k=-2, so the equation begins as y = a(x-4)^2 - 2.
To find the value of 'a', we use the fact that when x=0 (the y-intercept), y=6. Plugging these values in gives us 6 = a(0-4)^2 - 2, which simplifies to 6 = 16a - 2. Solving for 'a' gives a = ½. Substituting back into our equation, we get y = ½(x-4)^2 - 2 as the equation of the parabola in vertex form.