Understanding the Axis of Symmetry
In the context of a quadratic equation, the axis of symmetry is a vertical line that divides the graph into two mirror images. It plays a crucial role in understanding the properties of the graph, particularly when it comes to identifying the vertex and the direction in which the parabola opens.
The Standard Form of Quadratic Equation
The standard form of a quadratic equation is given as:
y = ax^2 + bx + c
Here, a, b, and c are constants.
Finding the Axis of Symmetry
For any quadratic equation in this standard form, the equation of the axis of symmetry can be found using the formula:
x = -b / (2a)
In your case, the equation is:
y = 3x^2 + 6x + 22
From this equation, we can identify the values of a and b:
- a = 3
- b = 6
- c = 22 (though this value is not needed for finding the axis of symmetry)
Calculating the Axis of Symmetry
Now let’s plug the values of a and b into the axis of symmetry formula:
x = -b / (2a) = -6 / (2 * 3)
This simplifies to:
x = -6 / 6 = -1
Conclusion
Thus, the equation of the axis of symmetry for the graph of the quadratic equation y = 3x^2 + 6x + 22 is:
x = -1
This essentially means that if you were to draw a vertical line at x = -1, it would slice through the parabola in such a way that both halves would be symmetrical. This information can be particularly useful for graphing the function or analyzing its properties further.