The axis of symmetry for a quadratic function in the standard form f(x) = ax² + bx + c can be found using the formula:
x = -b / (2a)
In this case, the coefficients are:
- a = 2
- b = 4
- c = 5
Plugging in the values of a and b into the formula gives us:
x = -4 / (2 * 2) = -4 / 4 = -1
Thus, the axis of symmetry for the quadratic function f(x) = 2x² + 4x + 5 is x = -1.
This means that the parabola opens upwards and is symmetrical around the vertical line x = -1. Any point on one side of this line has a corresponding point on the other side, making it a key feature in the graph of the function.