The graph of x^2 - 12y = 12x - 12 is the graph of a(n) ________.
Parabola?
correct
Thank you
To determine the type of graph represented by the equation x^2 - 12y = 12x - 12, we need to analyze the equation.
First, we can rearrange the given equation to obtain the standard form of a quadratic equation:
x^2 - 12x - 12y = -12
Next, we group the x-terms and rewrite the equation as:
(x^2 - 12x) - 12y = -12
To complete the square, we need to add and subtract (12/2)^2 = 36 to the left side of the equation:
(x^2 - 12x + 36) - 12y = -12 + 36
Simplifying, we have:
(x - 6)^2 - 12y = 24
Now, we can move the constant term to the right side of the equation:
(x - 6)^2 = 12y + 24
Dividing both sides by 12, we obtain:
(x - 6)^2/12 = y + 2
Finally, we can rewrite the equation in the standard form of a parabola:
(y + 2) = (1/12)(x - 6)^2
From this analysis, we can conclude that the graph of the given equation, x^2 - 12y = 12x - 12, is the graph of a parabola.