Final answer:
The range of the function p(x)=2(x+3)^2-9 is y≥-9, determined by the vertex of the parabola, which is located at the coordinates (-3, -9).
Step-by-step explanation:
The range of the quadratic function p(x) = 2(x + 3)^2 - 9 can be found by looking at the transformation of the parent function f(x) = x^2. Since the coefficient of the squared term is positive (2), the parabola opens upwards, and the vertex of the parabola gives us the minimum value of the function. The coordinates of the vertex can be found by completing the square or by using the formula -b/(2a) for the x-coordinate, and then substituting this value back into the function to find the y-coordinate. Given that the vertex form of the function is already provided, the vertex is at (-3, -9), and the range is thus y ≥ -9.