To find the coordinates of the vertex for the quadratic function f(x) = x² + 4x – 10, we can use the vertex formula. For a quadratic function of the form f(x) = ax² + bx + c, the x-coordinate of the vertex can be calculated using:
x = -b / (2a)
In our case, a = 1, b = 4, and c = -10. Substituting these values into the formula gives:
x = -4 / (2 * 1) = -4 / 2 = -2
Now, to find the corresponding y-coordinate, we substitute x = -2 back into the function:
f(-2) = (-2)² + 4(-2) – 10 = 4 – 8 – 10 = -14
Thus, the coordinates of the vertex are (-2, -14). This point represents the minimum of the parabola since it opens upwards (a > 0).