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 \( x=1 \)

To create a quadratic function with the given solutions \( x=2 \) and \( x=1 \), you can start with the factored form: \( f(x) = a(x - 2)(x - 1) \). Expanding this gives: \[ f(x) = a(x^2 - 3x + 2) \] Now, let’s express this in standard form: \[ f(x) = a x^2 - 3a x + 2a \] Setting \( a = 1 \) for simplicity, we get: \[ f(x) = x^2 - 3x + 2 \] This is the quadratic function in standard form. So, in essence, you can easily plug in any value of \( a \) to stretch or compress your parabola, while keeping the roots intact!