The axis of symmetry is an essential feature of a quadratic function. For the function h(x) = 2x2 + 12x – 3, the axis of symmetry can be determined using the formula:
x = -b / (2a)
In this quadratic equation, a is the coefficient of x2, and b is the coefficient of x. Here, we have:
- a = 2
- b = 12
Substituting these values into the axis of symmetry formula:
x = -12 / (2 * 2)
Simplifying this gives:
x = -12 / 4 = -3
Thus, the axis of symmetry for the quadratic function h(x) = 2x2 + 12x – 3 is x = -3.
This means that the parabola opens either upwards or downwards, and the line x = -3 divides the parabola into two mirror-image halves.