To find the axis of symmetry for the quadratic function given by the equation y = 2x² + 4x + 6, we use the formula for the axis of symmetry of a parabola, which is given by:
x = -b / 2a
In this equation, a and b are the coefficients from the standard form of a quadratic equation y = ax² + bx + c.
For our function:
- a = 2
- b = 4
- c = 6
Now, substituting the values of a and b into the axis of symmetry formula, we get:
x = -4 / (2 * 2) = -4 / 4 = -1
This means the equation representing the axis of symmetry for the function is:
x = -1
This vertical line, x = -1, indicates that the parabola opens upwards, and it is symmetric around this line.