The axis of symmetry for a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:
x = -b / (2a)
In your function, f(x) = x² + 9x + 21, we identify the coefficients:
- a = 1
- b = 9
- c = 21
Now, plug the values of a and b into the formula:
x = -9 / (2 * 1)
This simplifies to:
x = -9 / 2
Thus, the axis of symmetry for the function f(x) = x² + 9x + 21 is:
x = -4.5
This line x = -4.5 divides the parabola into two mirror-image halves.