I'm trying to put this parabola in standard form which is: (y-k)^2=4p(x-h)
The equation is x=(1/12)(y-2)^2 +6
Here is what i have so far:
x=(1/12)(y-2)^2 +6
-6 -6
x-6=(1/12)(y-2)^2
*12 *12
Would it be
12x-6 OR 12x-72?
thanks
from
x-6=(1/12)(y-2)^2
multiply both sides by 12
12(x-6) = (y-2)^2 , which of course is
(y-2)^2 = 12(x-6) , leave it like that, or you lose the form requested.
To put the equation x = (1/12)(y-2)^2 + 6 into standard form (y-k)^2 = 4p(x-h), you need to expand the equation and rearrange it. Here are the steps:
1. Start with the given equation: x = (1/12)(y-2)^2 + 6
2. Multiply both sides of the equation by 12 to eliminate the fraction:
12x = (y-2)^2 + 72
3. Expand the square on the right side using the perfect square formula:
12x = y^2 - 4y + 4 + 72
4. Combine like terms on the right side:
12x = y^2 - 4y + 76
5. To complete the square on the right side, we need to determine the value of k (the y-coordinate of the vertex). Since the equation is in the form (y-k)^2, we know that k = -4/(2*1) = -2.
6. Add and subtract (-2)^2 = 4 inside the parentheses to create a perfect square trinomial on the right side:
12x = y^2 - 4y + 76 + 4 - 4
7. Rearrange the terms:
12x = (y^2 - 4y + 4) + 76 - 4
8. Factor the perfect square trinomial inside the parentheses:
12x = (y-2)^2 + 72
9. Now we have the equation in the form (y-k)^2 = 4p(x-h), where h = 0 and p = 18. Therefore, the standard form of the equation is:
(y-2)^2 = 4*18*(x-0)
So, the correct equation in standard form is:
(y-2)^2 = 72(x)
To put the given equation x = (1/12)(y-2)^2 + 6 into standard form, which is (y-k)^2 = 4p(x-h), you need to expand the equation and rearrange the terms. Let's go step by step:
Starting equation: x = (1/12)(y-2)^2 + 6
First, let's isolate the term (y-2)^2 by subtracting 6 from both sides of the equation:
x - 6 = (1/12)(y-2)^2
Next, multiply both sides of the equation by 12 to get rid of the fraction:
12(x - 6) = (y-2)^2
Now, we can expand the square on the right-hand side by applying the square of a binomial formula:
12x - 72 = y^2 - 4y + 4
Finally, put the equation in standard form by moving all terms to one side:
y^2 - 4y + 4 = 12x - 72
Hence, the equation x = (1/12)(y-2)^2 + 6 can be put in standard form as y^2 - 4y + 4 = 12x - 72.
So the correct answer would be 12x - 72, not 12x - 6.