Put the quadratic into vertex form and state the coordinates of the vertex.y, equals, x, squared, plus, 8, x, plus, 12y=x 2 +8x+12

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

To convert the given quadratic y=x²+8x+12 into vertex form, we complete the square:

1. In the equation y=x²+8x+12, the coefficient of x² is 1, the coefficient of x is 8, and the constant term is 12.

2. To complete the square, we take half of the coefficient of x, square it, and add and subtract that value inside the square. Half of 8 is 4, and 4² is 16. So we add and subtract 16 inside the square:

   y=(x²+8x+16-16)+12

3. This simplifies to:

   y=((x+4)²-16)+12

4. Which further simplifies to:

   y=(x+4)²-4

So, the given quadratic in vertex form is y=(x+4)²-4.

The coordinates of the vertex (h,k) are given by the values that make the square in the equation zero. In this case, h=-4 and k=-4. So the vertex of the parabola is (-4,-4).