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The problem asks you to write a quadratic function with zeros at -1 and 6, using the variable \(x\) and in standard form, with a leading coefficient of 1.

To form the quadratic function from its zeros, we use the fact that if a quadratic function has roots (or zeros) at \(r_1\) and \(r_2\), the function can be written as:

\[
g(x) = a(x - r_1)(x - r_2)
\]

Given that the zeros are \(-1\) and \(6\), and the leading coefficient \(a = 1\), the function becomes:

\[
g(x) = (x + 1)(x - 6)
\]

Now, expand this expression:

\[
g(x) = (x + 1)(x - 6) = x^2 - 6x + x - 6 = x^2 - 5x - 6
\]

Thus, the quadratic function is:

\[
g(x) = x^2 - 5x - 6
\]

Would you like more details, or do you have any questions?

Here are 5 questions for further practice:
1. What is the quadratic function with zeros at 3 and -2?
2. How would you factor the quadratic \(x^2 + 2x - 8\)?
3. What is the vertex of the function \(g(x) = x^2 - 5x - 6\)?
4. How do you find the axis of symmetry of a quadratic function?
5. How would you graph the function \(g(x) = x^2 - 5x - 6\)?

**Tip:** When you know the roots of a quadratic, you can always write it in factored form and expand to get the standard form.

Write a quadratic function with zeros -1 and 6.

Learn how to write a quadratic function with zeros at -1 and 6, using standard algebraic techniques and factoring methods. This solution guides you through forming the equation and expanding it to standard form, suitable for students in Grades 8-10.

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