The coordinates of the vertex of the parabola represented by the equation y = x² + 2x – 3 can be determined by using the vertex formula for a quadratic function. A quadratic function can be expressed in the standard form as y = ax² + bx + c, where a, b, and c are constants.
In this case, we identify:
- a = 1
- b = 2
- c = -3
To find the x-coordinate of the vertex, we use the formula:
x = -b / (2a)
Substituting the values of a and b:
x = -2 / (2 * 1) = -1
Now that we have the x-coordinate, we can find the corresponding y-coordinate by substituting x = -1 back into the original equation:
y = (-1)² + 2(-1) – 3
y = 1 – 2 – 3
y = -4
Thus, the coordinates of the vertex of the parabola are (-1, -4). This point is significant as it represents the minimum value of the parabola since the parabola opens upwards (as indicated by a > 0).
In summary, for the quadratic equation y = x² + 2x – 3, the vertex is located at (-1, -4).