Find the vertex of quadratic relation by completing the square.y = x2 + 12x + 30

To find the vertex of the quadratic equation y = x² + 12x + 30, we need to complete the square. Here are the steps:

1. Rewrite the equation in the form of y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

2. To do this, we first need to complete the square for the equation. The equation is currently in the form y = x² + bx + c. We can rewrite this as y = (x² + 12x) + 30.

3. To complete the square, we need to add and subtract (b/2)² inside the parenthesis. In this case, b is 12, so (b/2)² = (12/2)² = 36.

4. Now, rewrite the equation as y = (x² + 12x + 36 - 36) + 30.

5. Simplify the equation to get y = (x + 6)² - 6 + 30.

6. Finally, simplify further to get y = (x + 6)² + 24.

So, the vertex of the parabola is (-6, 24).

Sure, here are the steps to find the vertex of the quadratic relation y = x² + 12x + 30 by completing the square:

1. The standard form of a quadratic equation is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

2. To rewrite the given equation in this form, we need to complete the square for the x terms. The equation is currently in the form y = x² + 12x + 30.

3. The first step in completing the square is to find the value that completes the square for the x² and 12x terms. This value is (b/2)², where b is the coefficient of the x term. In this case, b is 12, so (b/2)² = (12/2)² = 36.

4. We add and subtract this value inside the square to get: y = (x² + 12x + 36) - 36 + 30.

5. This simplifies to y = (x + 6)² - 6.

6. So, the vertex of the parabola is at (-6, -6).