The line of symmetry for a parabola can be found using the formula:
x = -b / (2a)
In the given equation, y = x² + 10x + 25, we can identify the coefficients:
- a = 1 (the coefficient of x²)
- b = 10 (the coefficient of x)
- c = 25 (the constant term)
Now, we can substitute these values into the formula:
x = -10 / (2 * 1) = -10 / 2 = -5
Therefore, the line of symmetry for the parabola is x = -5.
This means that if you were to draw a vertical line at x = -5, the parabola would be a mirror image on either side of this line. It’s important to note that the line of symmetry helps identify the vertex of the parabola and plays a crucial role in understanding its shape and trajectory.
In conclusion, for the parabola described by the equation y = x² + 10x + 25, the line of symmetry is x = -5.