Where is the vertex of the graph of

y = x2 + 6x - 2?

Complete the square.

y = x2 + 6x - 2 = x^2 + 6x + 9 -11
= (x+3)^2 - 11

The lowest value of y occurs where x+3 = 0.
Solve for x and then y

To find the vertex of the graph of a quadratic function, you can follow these steps:

Step 1: Recall the vertex form of a quadratic function, which is given by y = a(x - h)^2 + k. In this form, (h, k) represents the coordinates of the vertex.

Step 2: Convert the given quadratic function, y = x^2 + 6x - 2, into the vertex form by completing the square.

y = x^2 + 6x - 2

To complete the square, add and subtract the square of half the coefficient of the x-term (which is (6/2)^2 = 9) inside the brackets:

y = x^2 + 6x + 9 - 9 - 2

Simplify the equation:

y = (x + 3)^2 - 11

Step 3: Now we can see that the vertex form of the quadratic function is y = (x + 3)^2 - 11. The vertex is given by the values of (h, k).

From the equation, we can see that h = -3 and k = -11.

Therefore, the vertex of the graph of y = x^2 + 6x - 2 is (-3, -11).