Final answer:
The range of the quadratic function y = x² + 2x - 15 is all real numbers y ≥ -16, as the vertex of the parabola is the minimum point at y = -16.
Step-by-step explanation:
The range of the quadratic function y = x² + 2x - 15 is determined by finding the vertex of the parabola that this function represents since the vertex represents either the maximum or minimum point of the graph. For a quadratic function in the form y = ax² + bx + c, the x-coordinate of the vertex is found using -b/(2a). Substituting the values from our given quadratic function into this formula, we get -2/(2· 1) which simplifies to -1. Then we calculate the y-coordinate of the vertex by substituting x = -1 back into the original equation, yielding y = (-1)² + 2·(-1) - 15 = -16. Since the coefficient of the x² term is positive, the parabola opens upwards, indicating that the vertex represents the minimum point. Therefore, the range of the function is all real numbers y such that y ≥ -16.