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.

The given equation is x = y² + 10y + 22.

To convert this into vertex form, we need to complete the square for the y terms.

Here are the steps:

1. Group the y terms together: x = (y² + 10y) + 22.

2. To complete the square, we need to add and subtract (b/2)² inside the parenthesis, where b is the coefficient of y. Here, b = 10, so (b/2)² = (10/2)² = 25.

3. Add and subtract 25 inside the parenthesis: x = (y² + 10y + 25 - 25) + 22.

4. Simplify the equation: x = ((y + 5)² - 25) + 22.

5. Simplify further to get the vertex form: x = (y + 5)² - 3.

So, the vertex form of the given equation is x = (y + 5)² - 3.

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.

The given equation is x = y² + 10y + 22.

To convert this into vertex form, we need to complete the square for the y terms.

Here are the steps:

1. Group the y terms together: x = (y² + 10y) + 22.

2. To complete the square, we need to add and subtract (b/2)² inside the parenthesis, where b is the coefficient of y. Here, b = 10, so (b/2)² = (10/2)² = 25.

3. Add and subtract 25 inside the parenthesis: x = (y² + 10y + 25 - 25) + 22.

4. Simplify the equation: x = ((y + 5)² - 25) + 22.

5. Simplify further to get the vertex form: x = (y + 5)² - 3.

So, the vertex form of the given equation is x = (y + 5)² - 3.

Knowee AI · Accepted Answer

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.

The given equation is x = y² + 10y + 22.

To convert this into vertex form, we need to complete the square for the y terms.

Here are the steps:

1. Group the y terms together: x = (y² + 10y) + 22.

2. To complete the square, we need to add and subtract (b/2)² inside the parenthesis, where b is the coefficient of y. Here, b = 10, so (b/2)² = (10/2)² = 25.

3. Add and subtract 25 inside the parenthesis: x = (y² + 10y + 25 - 25) + 22.

4. Simplify the equation: x = ((y + 5)² - 25) + 22.

5. Simplify further to get the vertex form: x = (y + 5)² - 3.

So, the vertex form of the given equation is x = (y + 5)² - 3.

The standard form of the equation of a parabola is x = y2 + 10y + 22.What is the vertex form of the equation?

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