Determine the turning point of the parabola f(x) = -3x^2=12x-4

Answer 1

To find the turning point of the parabola, we need to complete the square for the given equation:

f(x) = -3x^2 + 12x - 4

We first factor out the coefficient of x^2 from the first two terms:

f(x) = -3(x^2 - 4x) - 4

Next, we complete the square inside the parentheses by taking half of the coefficient of x (-4), squaring it, and adding it inside the parentheses:

f(x) = -3(x^2 - 4x + 4 - 4) - 4
f(x) = -3(x^2 - 4x + 4) + 12 - 4
f(x) = -3(x - 2)^2 + 8

Therefore, the turning point of the parabola is at the point (2, 8).