A quadratic function has its vertex at the point $$ (-5,-4) $$. The function passes through the point $$ (8,-3) $$. When written in vertex form, the function is $$ f(x)=a(x-h)^{2}+k $$, where: $$ a= $$ $$ h= $$ $$ k= $$

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To find the quadratic function in vertex form $$ f(x) = a(x - h)^2 + k $$, we can follow these steps:

1. **Identify the vertex**: From the problem, we know the vertex is at the point $$ (h, k) = (-5, -4) $$. Therefore, we have:
   - $$ h = -5 $$
   - $$ k = -4 $$

2. **Substitute the vertex into the vertex form**: The function can now be partially written as:
   $$
   f(x) = a(x + 5)^2 - 4
   $$

3. **Use the point that the function passes through**: We know the function passes through the point $$ (8, -3) $$. We can substitute $$ x = 8 $$ and $$ f(x) = -3 $$ into the equation to find $$ a $$:
   $$
   -3 = a(8 + 5)^2 - 4
   $$

4. **Calculate $$ (8 + 5)^2 $$**:
   $$
   8 + 5 = 13 \quad \Rightarrow \quad 13^2 = 169
   $$

5. **Substitute back into the equation**:
   $$
   -3 = a(169) - 4
   $$

6. **Solve for $$ a $$**:
   $$
   -3 + 4 = 169a \quad \Rightarrow \quad 1 = 169a \quad \Rightarrow \quad a = \frac{1}{169}
   $$

Now we have all the values:
- $$ a = \frac{1}{169} $$
- $$ h = -5 $$
- $$ k = -4 $$

Thus, the final answer is:
- $$ a = \frac{1}{169} $$
- $$ h = -5 $$
- $$ k = -4 $$
$$ a = \frac{1}{169} $$, $$ h = -5 $$, $$ k = -4 $$.

A quadratic function has its vertex at the point \( (-5,-4) \). The function passes through the point \( (8,-3) \). When written in vertex form, the function is \( f(x)=a(x-h)^{2}+k \), where: \( a= \) \( h= \) \( k= \)

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