Re-write the quadratic function below in Standard Form $$ y=-2(x-4)^{2}+8 $$

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To rewrite the quadratic function $$ y = -2(x-4)^{2} + 8 $$ in standard form, we need to expand the expression and simplify it. The standard form of a quadratic function is given by:

$$
y = ax^2 + bx + c
$$

where $$ a $$, $$ b $$, and $$ c $$ are constants.

Let's proceed step by step:

1. **Expand the squared term**: 
   $$
   (x-4)^{2} = x^{2} - 8x + 16
   $$

2. **Substitute back into the equation**:
   $$
   y = -2(x^{2} - 8x + 16) + 8
   $$

3. **Distribute $$-2$$**:
   $$
   y = -2x^{2} + 16x - 32 + 8
   $$

4. **Combine like terms**:
   $$
   y = -2x^{2} + 16x - 24
   $$

Now, we have the quadratic function in standard form:

$$
y = -2x^{2} + 16x - 24
$$

Thus, the standard form of the given quadratic function is:

$$
y = -2x^{2} + 16x - 24
$$
The standard form of the quadratic function is $$ y = -2x^{2} + 16x - 24 $$.

Re-write the quadratic function below in Standard Form \[ y=-2(x-4)^{2}+8 \]

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