Write a quadratic function in standard form whose graph has the given characteristics.

vertex: $(1,\ 9)$ ; passes

To write a quadratic function in standard form, we need to use the **vertex form** of a quadratic equation, which is given by:

\[
f(x) = a(x - h)^2 + k
\]

where $ (h, k) $ is the vertex of the parabola. Given the vertex $ (1, 9) $, the equation becomes:

\[
f(x) = a(x - 1)^2 + 9
\]

Next, we need an additional point on the graph to determine the value of $a$. You mentioned "passes", but it seems like the specific point the parabola passes through is missing. Can you provide the coordinates of that point? That way, we can determine the value of $a$ and fully express the quadratic function in standard form.

Would you like to provide the point, or have any questions so far?

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Here are 5 questions to further your understanding:
1. What is the importance of the vertex form of a quadratic function?
2. How do you convert from vertex form to standard form?
3. Can a quadratic function have more than one vertex?
4. What effect does the parameter $a$ have on the graph of a quadratic function?
5. How would you find the axis of symmetry from a quadratic function?

**Tip:** The vertex form is very useful when identifying the maximum or minimum of a quadratic function easily.

Write a quadratic function in standard form whose graph has the given characteristics: vertex (1, 9); passes.

Explore how to write a quadratic function in standard form with the vertex (1, 9). This guide covers the key concepts of vertex and standard forms, along with solving steps. Ideal for students in Grades 9-11.

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