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 in the standard form f(x) = ax² + bx + c, the x-coordinate of the vertex is given by:
x = -b / (2a)
In our case, a = 1 and b = 4. Plugging these values into the formula gives us:
x = -4 / (2 * 1) = -4 / 2 = -2
Now that we have the x-coordinate of the vertex, we can find the corresponding y-coordinate by substituting x = -2 back into the function:
f(-2) = (-2)² + 4(-2) – 10
f(-2) = 4 – 8 – 10 = -14
Therefore, the coordinates of the vertex are (-2, -14). This vertex represents the minimum point of the parabola described by the function.