A quadratic function is a type of polynomial function that can be expressed in the standard form f(x) = ax^2 + bx + c , where a , b , and c are constants, and a ≠ 0 . The graph of a quadratic function is a parabola, which can open either upward or downward depending on the sign of a . Quadratic functions have important features, including the vertex, which is the highest or lowest point of the parabola, and the axis of symmetry, a vertical line that divides the parabola into two mirror-image halves. The solutions to the equation ax^2 + bx + c = 0 are called the roots, and they can be found using methods such as factoring, completing the square, or the quadratic formula.