Question

The general form of a parabola is x2−6x−2y+7=0. What is the standard form of this parabola?

Answer 1

Hi,

Explanation:

To find the standard form of the given parabola x^2 - 6x - 2y + 7 = 0, we need to rearrange the equation.

The standard form of a parabola is y = ax^2 + bx + c, where a, b, and c are constants.

Step 1: Move all terms to one side of the equation:

x^2 - 6x - 2y + 7 = 0

Rearrange the terms:

x^2 - 2y - 6x + 7 = 0

Step 2: Group the x-terms together and the constant terms together:

(x^2 - 6x) - 2y + 7 = 0

Step 3: Complete the square for the x-terms:

(x^2 - 6x + 9) - 2y + 7 = 9

(x - 3)^2 - 2y + 7 = 9

Step 4: Simplify and rearrange the equation:

(x - 3)^2 - 2y = 2

Therefore, the standard form of the parabola is (x - 3)^2 - 2y = 2.

or (x-3)²=2(y+1)

Answer 2

Explanation:

Using 'standard form' definition I found on the internet:

x^2 - 6x + 7 = 2y Complete the square for 'x' on the L side

(x-3)^2 - 2 = 2y

(x-3)^2 = 2y + 2

(x-3)^2 = 2 ( y+1)