To rewrite the quadratic function $y = -2(x - 6)^2 + 5$ in standard form, we need to expand the expression and simplify it. The standard form of a quadratic function is:

$y = ax^2 + bx + c$

Here’s how we can do it step by step:

1. Expand the square:
   $(x - 6)^2 = (x - 6)(x - 6) = x^2 - 12x + 36$

2. Multiply by -2:
   $-2(x^2 - 12x + 36) = -2x^2 + 24x - 72$

3. Add the constant 5:
   $y = -2x^2 + 24x - 72 + 5$

4. Simplify the constants:
   $y = -2x^2 + 24x - 67$

So, the quadratic function in standard form is:

$y = -2x^2 + 24x - 67$

Let me know if you need more details or have any questions!

Follow-up Questions:

1. What does the "vertex form" of a quadratic function represent?
2. How do you find the vertex of a parabola given its standard form?
3. How would the graph change if the coefficient of $x^2$ were positive instead of negative?
4. How do you determine the axis of symmetry from the standard form?
5. What is the significance of the constant term in a quadratic function?

Tip: To quickly find the vertex of a quadratic in standard form, use the formula $x = \frac{-b}{2a}$, where $a$ and $b$ are the coefficients from $y = ax^2 + bx + c$.