1. **Problem:** Find the vertex of the parabola given by the equation $$y = x^2 + 2x - 3$$. 2. **Formula for vertex:** The vertex of a parabola in the form $$y = ax^2 + bx + c$$ is given by the coordinates $$\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$ where $$f(x)$$ is the quadratic function. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 2$$, and $$c = -3$$. 4. **Calculate x-coordinate of vertex:** $$x = -\frac{b}{2a} = -\frac{2}{2 \times 1} = -1$$ 5. **Calculate y-coordinate of vertex:** Substitute $$x = -1$$ into the equation: $$y = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4$$ 6. **Vertex coordinates:** The vertex is at $$(-1, -4)$$. 7. **Answer:** The correct choice is **b) [ -1 , -4 ]**.