Final answer:
To write the equation x² - 4x + 2y + 12 = 0 in standard form for a parabola, rearrange the equation to isolate the x terms and complete the square. The standard form is (x - 2)² = -2y - 8.
Step-by-step explanation:
The given equation is x² - 4x + 2y + 12 = 0.
To write this equation in standard form for a parabola, we need to isolate the terms involving x on one side of the equation. Rearranging the equation, we get x² - 4x = -2y - 12.
Next, we can complete the square for the x terms by adding the square of half the x coefficient. Half of -4 is -2, so we add (-2)² = 4 to both sides of the equation, resulting in x² - 4x + 4 = -2y - 8.
Finally, we can rewrite the left side of the equation as a perfect square: (x - 2)². So, the standard form of the parabola equation is (x - 2)² = -2y - 8.