Name the coordinates of the vertex of the parabola given by the equation; y = (x + 1) ^ 2

First, find the x coordinate of the vertex of the parabola. The x coordinate of the point of the vertex of the parabola is found by the formula: x = – b / 2a;

We expand our equations according to the formula for abbreviated multiplication of the square of the sum:

(x + 1) ^ 2 = x ^ 2 + 2x + 1, from the equation we see that a = 1, b = 2, c = 1 (based on the general form of the quadratic equation ax ^ 2 + bx + c), we find x :

x = – 2/2 * 1 = -1;

To find the coordinate at the vertex of the parabola, we find the value of the function at the value of the argument x = -1:

y = (-1 + 1) ^ 2 = 0;

The vertex of the parabola of this quadratic equation lies at the point (-1; 0).

Answer: (-1; 0).