Quadratic Functions

We can get confused between quadratic equations and quadratic functions. There is almost no difference between a quadratic equation and a quadratic function when it comes to finding their roots, or graphing them.

A quadratic equation is a mathematical statement of equality in which the degree of the expression is 2. A quadratic function is an algebraic representation of the path of a parabola.

A quadratic function has the form of f(x) = (a quadratic expression).

Examples of quadratic functions are:
  • f(x) = x^2 + 2x + 1
  • f(x) = -2x^2 + 5x - 7
  • f(y) = y^2 - 3y
  • g(x) = 5x^2 + 4x + 1
Roots of a quadratic function
The roots of a quadratic function are the two solutions for x in the quadratic function when it is equated to zero. These are the two x-intercepts of the parabola. Learn more about the roots of a quadratic function/equation here.

Forms of a quadratic function
Just as a quadratic equation can be written in different forms, similarly a quadratic function can be written in those forms as well. So the different forms of a quadratic function are called the general form, the vertex form and the intercept form. You can learn more about different forms of a quadratic function/equation here.

Graphing quadratic functions
Graphing quadratic functions is similar to graphing quadratic equations. The graph of a quadratic function/equation is in the shape of a U shaped curve called a parabola. You can learn more about graphing a quadratic here.

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