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.

Example

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.

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.

ax² + bx + c = 0