Quadratic function

A quadratic is a polynomial where the term with the highest power has a degree of 2.

The parent function of quadratics is:

f(x) = x2

Quadratic functions follow the standard form:

f(x) = ax2 + bx + c

If ax2 is not present, the function will be linear and not quadratic. Quadratic functions make a parabolic U-shape on a graph. If a is negative, the parabola is flipped upside down.


f(x) = -x2 + 2x + 3

Quadratic functions are symmetric about a vertical axis of symmetry. This axis of symmetry can be calculated using the formula:

x =

The vertex is the point found on the axis of symmetry. Because you know the x coordinate of the vertex from the axis of symmetry, you can plug that value into the function to find the y-coordinate.


f(x) = x2 - 2x - 3
a = 1; b = -2; c = -3
x = = = 1
Axis of symmetry at x = 1

The quadratic equation is an equation where you set the quadratic function equal to 0. Solving the quadratic equation yields the zeroes, or solutions, of the quadratic.

ax2 + bx + c = 0

See also parabola, vertex of a parabola, quadratic formula, vertex form.