The standard form of a quadratic function is:
The graph of any quadratic function is a parabola. The simplest form of the quadratic function is where the coefficients b and c are both zero. Then the graph is a parabola with the vertex at the origin {0, 0} and is symmetric about the y-axis. If the coefficient a, is positive, the vertex is a minimum with the parabola pointing up; if negative, the vertex is a maximum with the parabola pointing down.f(x) = ax2 + bx + c, where a ≠ 0
Axis crossing
The points where a function crosses the Cartesian coordinate axes are useful in graphing. The point of crossing the y-axis can be found by setting the value of x to zero. The zeroes of a function, the values of x which make it take a value of zero, are the points of crossing the x-axis.
Example, find the axis crossings of f(x) = x2 - 2x - 3:
Then, f(x) crosses the y-axis at {0, -3} and the x-axis at {-1, 0} and {3, 0}.f(0) = 02 + 0 - 3 = -3 0 = x2 - 2x - 3 = (x + 1)(x - 3)