Final answer:
The coordinates of the turning point for the curve y = 2x² - 16x + 38, found by completing the square, are (4, 6).
Step-by-step explanation:
To find the coordinates of the turning point of the curve y = 2x² - 16x + 38, we use the technique of completing the square.
First, we divide the equation by the coefficient of the x² term to make it 1:
y/2 = x² - 8x + 19
Next, we work out the square by halving the coefficient of x, then squaring it, and adding and subtracting this number inside the parenthesis:
y/2 = (x - 4)² - 16 + 19
y = 2(x - 4)² + 6
The vertex form is now y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
In our equation, h = 4 and k = 6, so the coordinates of the turning point are (4, 6).