To write a quadratic function with roots $11$ and $P$, we can use the fact that the general form of a quadratic function with roots $r_1$ and $r_2$ is:

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

Since the leading coefficient $a = 1$ and the roots are $11$ and $P$, the quadratic function is:

$f(x) = (x - 11)(x - P)$

Now, expand the expression:

$f(x) = x^2 - (11 + P)x + 11P$

Thus, the quadratic function is:

$f(x) = x^2 - (11 + P)x + 11P$

Would you like a step-by-step breakdown of how I expanded it?

Here are 5 questions related to this:

1. What is the effect of changing the leading coefficient on the quadratic function?
2. How do you find the vertex of a quadratic function from its equation?
3. What is the relationship between the sum and product of the roots and the quadratic coefficients?
4. How can you find the axis of symmetry for a quadratic function?
5. How do transformations like vertical shifts affect the graph of a quadratic function?

Tip: The sum of the roots of a quadratic function $ax^2 + bx + c = 0$ is given by $-\frac{b}{a}$, and the product is $\frac{c}{a}$.