Write the equation of a quadratic function with the given solutions. Use standard form $$ f(x)=a x^{2}+b x+c $$. $$ x=2 $$ and $$ x=1 $$

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1. The quadratic function with roots $$ x=2 $$ and $$ x=1 $$ can be written in factored form as:
   $$
   f(x)=a(x-2)(x-1)
   $$
   where $$ a $$ is any non-zero constant.

2. To convert this into standard form $$ f(x)=ax^2+bx+c $$, we first expand the factors:
   $$
   f(x)=a\left[(x-2)(x-1)\right]=a\left[x^2 - x - 2x + 2\right]=a\left[x^2 - 3x + 2\right]
   $$

3. Distributing the constant $$ a $$ gives:
   $$
   f(x)=ax^2 - 3ax + 2a
   $$

4. Choosing $$ a=1 $$ for simplicity, the quadratic function becomes:
   $$
   f(x)=x^2-3x+2
   $$
The quadratic function with roots $$ x=2 $$ and $$ x=1 $$ in standard form is: $$ f(x) = x^2 - 3x + 2 $$

Write the equation of a quadratic function with the given solutions. Use standard form \( f(x)=a x^{2}+b x+c \). \( x=2 \) and \( x=1 \)

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