What is the standard form of the quadratic function that has a vertex of (-3, -27)?

To find the standard form of a quadratic function with a vertex, you need to use the vertex form of the equation and then convert it to standard form. The vertex form of a quadratic function is given by:

y = a(x - h)^2 + k

Where (h, k) represents the coordinates of the vertex.

In this case, the vertex is (-3, -27), so we can write the equation as:

y = a(x - (-3))^2 + (-27)

Simplifying this expression, we get:

y = a(x + 3)^2 - 27

Now, to convert it into the standard form (ax^2 + bx + c), let's expand and simplify:

y = a(x^2 + 6x + 9) - 27
y = ax^2 + 6ax + 9a - 27

The standard form requires that we have only a single constant term. To achieve this, we can rewrite the equation as:

y = ax^2 + 6ax + (9a - 27)

So, the standard form of the quadratic function with a vertex of (-3, -27) is:

y = ax^2 + 6ax + (9a - 27)

Note: The value of 'a' is unknown and needs to be determined using additional information or constraints.