Find the vertex of the parabola whose equation is y = x² + 6x + 2.

Solution:

We have to find the coordinates of the vertex of the parabola.

For any equation of the type y = ax² + bx + c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is y = x² + 6x + 2

Here, a = 1, b = 6 and c = 2

So, h = -6/2(1)

h = -6/2

h = -3

4ac = 4(1)(2)

4ac = 8

So, k = [8 - (6)²]/4(1)

k = (8 - 36)/4

k = -28/4

k = -7

Therefore, the coordinates of the vertex is (h, k) = (-3, -7).

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Find the vertex of the parabola whose equation is y = x² + 6x + 2.

Summary:

The vertex of the parabola whose equation is y = x² + 6x + 2 is (-3, -7).