The axis of symmetry for a quadratic function can be determined using the formula:
x = -b / (2a)
In the function f(x) = x² + 9x + 21, the coefficients are:
- a = 1
- b = 9
- c = 21
Plugging the values of a and b into the axis of symmetry formula:
x = -9 / (2 * 1)
This simplifies to:
x = -9 / 2
Thus, the axis of symmetry for the function is:
x = -4.5
This means that if you were to draw the graph of this quadratic function, it would be symmetric about the line x = -4.5.
Understanding this concept helps not only in graphing the quadratic functions but also in finding the vertex, which can be further explored as:
- The vertex is the highest or lowest point of the parabola depending on its orientation.
- For this function, since the coefficient of x² is positive, the parabola opens upwards, confirming that the vertex will be the minimum point.