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The problem asks for the equation of a parabola in vertex form that has the same shape as either \( f(x) = 5x^2 \) or \( g(x) = -5x^2 \), but with a given minimum of 0 at \( x = 3 \).

### Key Points:
1. **Shape of the parabola**: The phrase "same shape" implies that the coefficient of \( x^2 \) should be the same. Since the graph must have a minimum, it will take the form of \( f(x) = 5x^2 \) (as the positive sign ensures a parabola opening upwards with a minimum).
   
2. **Vertex form of a parabola**: The vertex form of a parabola is
   \[
   h(x) = a(x - h)^2 + k
   \]
   where \( (h, k) \) is the vertex of the parabola. 

3. **Vertex information**: The problem gives that the minimum is 0 at \( x = 3 \), meaning the vertex is at \( (3, 0) \). Therefore, \( h = 3 \) and \( k = 0 \).

### Equation Derivation:
- Using the vertex form \( h(x) = a(x - h)^2 + k \),
- The vertex is at \( (3, 0) \), so \( h(x) = a(x - 3)^2 \).
- The parabola has the same shape as \( f(x) = 5x^2 \), so \( a = 5 \).

Thus, the equation is:
\[
h(x) = 5(x - 3)^2
\]

Let me know if you'd like further clarification, or if you have any questions.

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Here are 5 related questions:
1. How would the equation change if the minimum was at a different point, such as \( x = -2 \)?
2. What would the equation look like if the parabola had a maximum instead of a minimum?
3. How does the value of \( a \) affect the steepness of the parabola?
4. What happens if the coefficient \( a \) becomes negative?
5. How do you convert a standard form quadratic equation into vertex form?

**Tip**: In a quadratic equation, the sign of the leading coefficient \( a \) determines whether the parabola opens upwards or downwards.

Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 5x^2 or g(x) = -5x^2, but with the given minimum. Minimum = 0 at x = 3.

Learn how to write the equation of a parabola in vertex form with a given minimum at x = 3. Explore key concepts like vertex form and quadratic equations. Suitable for students in Grades 9-10.

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