To write a quadratic function with roots $20$ and $P$, we can use the fact that if a quadratic equation has roots $r_1$ and $r_2$, the equation can be written as:

$f(x) = a(x - r_1)(x - r_2)$

where $a$ is the leading coefficient. Given that the leading coefficient is $1$, $a = 1$, and the roots are $20$ and $P$, we can write the quadratic function as:

$f(x) = (x - 20)(x - P)$

Expanding this expression:

$f(x) = x^2 - (20 + P)x + 20P$

Thus, the quadratic function with roots $20$ and $P$ is:

$f(x) = x^2 - (20 + P)x + 20P$

Would you like more details or have any questions?

Related Questions:

1. How do you find the roots of a quadratic equation using the quadratic formula?
2. What are the characteristics of a quadratic function's graph?
3. How does changing the leading coefficient affect the shape of a quadratic graph?
4. How can you determine if a quadratic function has real or complex roots?
5. How do you complete the square to rewrite a quadratic function?

Tip:

When a quadratic function is factored as $(x - r_1)(x - r_2)$, the roots $r_1$ and $r_2$ correspond to the x-intercepts of the function's graph.