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### Part (a)
We are asked to express the quadratic equation \( 2x^2 + px + q \) in the form \( a(x + b)^2 + c \), which is the **completed square** form.

We will complete the square for the expression \( 2x^2 + px + q \).

1. **Factor out 2 from the first two terms**:  
   \( 2(x^2 + \frac{p}{2}x) + q \)

2. **Complete the square for the expression inside the parentheses**:
   - Take half of the coefficient of \(x\) inside the parentheses, which is \( \frac{p}{2} \),

Express 2x^2 + px + q in the form a(x + b)^2 + c and find the values of p and q for the curve y = 2x^2 + px + q that has a minimum point at (3, -2).

Learn how to express the quadratic equation 2x^2 + px + q in completed square form and find the values of p and q when the curve y = 2x^2 + px + q has a minimum point at (3, -2). This problem covers key algebraic concepts such as completing the square and using the vertex of a parabola.

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