The vertex form of a parabola's equation is given by x = a(y-h)² + k, where (h,k) is the vertex of the parabola.

In the given standard form equation x = y² + 10y + 22, we can complete the square to convert it into vertex form.

The square completes by taking half of the coefficient of y, squaring it and adding and subtracting it inside the equation.

Half of 10 is 5, and 5² is 25. So, we add and subtract 25 inside the equation.

x = y² + 10y + 25 - 25 + 22

This simplifies to:

x = (y + 5)² - 3

So, the vertex form of the equation is x = (y + 5)² - 3, which corresponds to option D.

Question

The vertex form of a parabola's equation is given by x = a(y-h)² + k, where (h,k) is the vertex of the parabola.

In the given standard form equation x = y² + 10y + 22, we can complete the square to convert it into vertex form.

The square completes by taking half of the coefficient of y, squaring it and adding and subtracting it inside the equation.

Half of 10 is 5, and 5² is 25. So, we add and subtract 25 inside the equation.

x = y² + 10y + 25 - 25 + 22

This simplifies to:

x = (y + 5)² - 3

So, the vertex form of the equation is x = (y + 5)² - 3, which corresponds to option D.

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