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The image contains several mathematical questions based on functions, transformations, and expressions. Here's a breakdown of each question:

1. **Question 01:**  
   The function \( f \) is defined by \( f(x) = 2x^2 - 7x + 2 \), \( x \in \mathbb{R} \).  
   (i) Express \( f \) in the form \( f(x) = a(x - h)^2 + k \), where \( a, h, k \) are constants.

2. **Question 02:**  
   The function is defined by \( h(x) = 6x^3 - 2x^2 + x + 1 \), \( x \in \mathbb{R} \).  
   (i) Express \( h(x) \) in the form of \( ax^3 + bx^2 + cx + d \), where \( a, b, c, d \) are constants.

3. **Question 03:**  
   The function is defined by \( f(x) = x^3 + 1.5x - 6 \), \( x \in \mathbb{R} \).  
   (i) Solve \( f(x) = 0 \) in the interval \( -3 \leq x \leq 3 \), using intervals of length 0.5.

4. **Question 04:**  
   The function is defined by \( g(x) = \frac{1}{x^2} - 4 \), \( x \in \mathbb{R} \).  
   (i) Express \( g(x) \) in the form of \( a \left( \frac{1}{x^2} \right) + b \), where \( a \) and \( b \) are constants.

5. **Question 05:**  
   The function is defined by \( f(x) = 1.2x - 7 \), \( x \in \mathbb{R} \).  
   (i) Express \( f(x) = 0 \) for \( x \in [-4, 5] \).

Would you like a detailed solution for any of these questions? Here are some related questions to deepen your understanding:

1. How can we complete the square for a quadratic function like in Question 01?
2. What method can be used to solve cubic equations such as in Question 03?
3. What are the transformations that take place when converting a general function to its vertex form?
4. How does the interval of approximation in Question 03 help in finding roots?
5. What are common techniques for expressing rational functions in terms of simpler constants?

**Tip:** To convert quadratic functions to vertex form, always start by factoring out the coefficient of \( x^2 \) and completing the square on the remaining terms.

The image contains several mathematical questions based on functions, transformations, and expressions.

Explore how to solve quadratic, cubic, and rational functions step by step. Learn how to express functions in different forms, solve for roots, and approximate solutions using interval methods. Suitable for students in Grades 9-12.

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