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) = x^{2}
Quadratic functions follow the standard form:
f(x) = ax^{2} + bx + c
If ax^{2} is not present, the function will be linear and not quadratic. Quadratic functions make a parabolic Ushape on a graph. If a is negative, the parabola is flipped upside down.
Example
f(x) = x^{2} + 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 ycoordinate.
Example

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.
ax^{2} + bx + c = 0
See also parabola, vertex of a parabola, quadratic formula, vertex form.