The equation for the graph in vertex form f(x)= a(x−h)2+k would have:

a=

h=

k=

The equation for a parabola in vertex form is given by:

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

Where:
- \(a\) controls the "stretch" or "compression" of the parabola and its direction (whether it opens upwards or downwards).
- \(h\) represents the x-coordinate of the vertex of the parabola.
- \(k\) represents the y-coordinate of the vertex of the parabola.

So, \(a\), \(h\), and \(k\) would be specific values based on the given equation. You would need the actual equation of a specific parabola to determine those values.

Would you like me to help you find \(a\), \(h\), and \(k\) for a particular equation or graph?

Here are some follow-up questions to consider:
1. Do you have a specific equation or graph in mind to find \(a\), \(h\), and \(k\)?
2. What is the role of the vertex in determining the shape of a parabola?
3. How does the value of \(a\) affect whether the parabola opens upwards or downwards?
4. What happens to the graph when you change the values of \(h\) and \(k\)?
5. Can you convert a parabola from standard form to vertex form?

**Tip:** To find \(h\) and \(k\), remember that they are the coordinates of the vertex of the parabola.

The equation for the graph in vertex form f(x) = a(x−h)^2 + k would have: a= h= k=

Learn how to identify the values of a, h, and k in the vertex form of a quadratic equation f(x) = a(x−h)^2 + k. This problem explains key concepts like parabolas, the vertex, and how the values of a, h, and k affect the graph. Ideal for students in Grades 8-10.

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