 Write a quadratic function with leading coefficient 1 that has roots of 20 and P. 

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.

Write a quadratic function with leading coefficient 1 that has roots of 20 and P.

Learn how to write a quadratic function with a leading coefficient of 1 and roots of 20 and P. This problem explores quadratic equations, factorization, and the relationship between roots and coefficients. Suitable for students in Grades 9-11.

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