Answer: bellow
Explain :
Y = a(x-h)^2 + k
where (h, k) represents the vertex of the parabola.
Let's start by expanding the equation:
Y = (1/3)(x^2 - 2x + 1) - 9
Y = (1/3)x^2 - (2/3)x + 1/3 - 9
Next, we need to complete the square for the x terms. To do this, we take half of the coefficient of x and square it. In this case, the coefficient of x is -2/3. Half of -2/3 is -1/3, and (-1/3)^2 is 1/9. We add and subtract 1/9 within the parentheses:
Y = (1/3)(x^2 - 2x + 1/9 - 1/9) + 1/3 - 9
Y = (1/3)((x - 1/3)^2 - 1/9) + 1/3 - 9
Now, we can simplify the equation:
Y = (1/3)(x - 1/3)^2 - 1/27 + 1/3 - 9
Y = (1/3)(x - 1/3)^2 - 1/27 + 9/27 - 27/27
Y = (1/3)(x - 1/3)^2 - 19/27
So, the equation Y = (1/3)(x-1)^2 - 9 is in vertex form, where the vertex is located at (1/3, -19/27).