To write a quadratic function with zeros $-1$ and $0$, we use the fact that a quadratic function can be expressed in terms of its zeros as:

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

Here:

• $r_1 = -1$
• $r_2 = 0$
• $a = 1$ (since the leading coefficient is specified to be 1)

Substituting these values, the function becomes:

$f(x) = 1(x - (-1))(x - 0)$

Simplify:

$f(x) = (x + 1)(x)$

Expand:

$f(x) = x^2 + x$

Thus, the quadratic function in standard form is:

$f(x) = x^2 + x$

Would you like additional details or have any questions?

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Related Questions:

1. What are the steps to graph this quadratic function?
2. How can we determine the vertex of this quadratic function?
3. What is the axis of symmetry for this function?
4. How does the sign of the leading coefficient affect the graph's shape?
5. Can you write another quadratic function with different zeros?

Tip: Always check your work by substituting the zeros back into the equation to confirm they satisfy the function.