Rewrite each of the quadratic equations in vertex form. $$ \text { 1. } f(x)=x^{2}+12 x-13 $$

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To rewrite the quadratic equation $$ f(x) = x^{2} + 12x - 13 $$ in **vertex form**, which is $$ f(x) = a(x - h)^2 + k $$, follow these steps:

1. **Complete the Square:**
   
   Start with the quadratic part of the equation:
   $$
   x^2 + 12x
   $$
   
   To complete the square, take half of the coefficient of $$ x $$ (which is 12), square it, and add and subtract this value inside the equation:
   $$
   x^2 + 12x + 36 - 36
   $$
   
   Here, $$ 36 = \left(\frac{12}{2}\right)^2 $$.

2. **Rewrite as a Perfect Square:**
   
   The expression $$ x^2 + 12x + 36 $$ is a perfect square:
   $$
   (x + 6)^2
   $$
   
   So, the equation becomes:
   $$
   f(x) = (x + 6)^2 - 36 - 13
   $$

3. **Simplify the Constants:**
   
   Combine the constants:
   $$
   -36 - 13 = -49
   $$
   
   Therefore, the vertex form of the equation is:
   $$
   f(x) = (x + 6)^2 - 49
   $$

**Final Answer:**
$$
f(x) = (x + 6)^2\; -\;49
$$
The vertex form of the quadratic equation $$ f(x) = x^{2} + 12x - 13 $$ is: $$ f(x) = (x + 6)^2 - 49 $$

Rewrite each of the quadratic equations in vertex form. \[ \text { 1. } f(x)=x^{2}+12 x-13 \]

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