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)
For the given function f(x) = 3x² + 18x + 7, we identify the coefficients:
- a = 3
- b = 18
- c = 7
Now, plug the values of a and b into the formula:
x = -18 / (2 * 3)
This simplifies to:
x = -18 / 6
So, we get:
x = -3
This means the axis of symmetry for the quadratic function f(x) = 3x² + 18x + 7 is x = -3. This line divides the parabola into two symmetrical halves, and any point on the parabola has a corresponding point at an equal distance from this line.