The axis of symmetry for a quadratic function is a vertical line that runs through the vertex of the parabola represented by the equation. For the general form of a quadratic equation, y = ax² + bx + c, the axis of symmetry can be found using the formula:
x = - rac{b}{2a}
In your case, we have the function:
y = 2x² + 4x + 6
Here, the coefficients are:
- a = 2
- b = 4
- c = 6
To find the axis of symmetry, we plug a and b into the formula:
x = - rac{4}{2 imes 2}
This simplifies to:
x = - rac{4}{4} = -1
Therefore, the equation representing the axis of symmetry for the function y = 2x² + 4x + 6 is:
x = -1
This means that the line x = -1 is the axis around which the parabola is symmetric. Any point on one side of this line will have a corresponding point on the other side that is an equal distance away from it.