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Quadratic function or 2nd degree function


Definition

It's called a quadratic function, or polynomial function of the 2nd degree, any function f IR to IR given by a law of the form f (x) = ax2 + bx + cwhere a, b and c are real numbers and a 0. Let's look at some examples of quadratic functions:

  • f (x) = 3x2 - 4x + 1, where a = 3, b = - 4 and c = 1
  • f (x) = x2 -1, where a = 1, b = 0 and c = -1
  • f (x) = 2x2 + 3x + 5 where a = 2, b = 3 and c = 5
  • f (x) = - x2 + 8x, where a = -1, b = 8 and c = 0
  • f (x) = -4x2where a = - 4, b = 0 and c = 0

Graphic

The graph of a 2nd degree polynomial function, y = ax2 + bx + c, with a 0 is a curve called parable.

For example, let's build the graph of the function y = x2 + x:

We first assign x some values, then calculate the corresponding value of y, and then connect the points thus obtained.

xy
-36
-22
-10
00
12
26

Note:

When graphing a quadratic function y = ax2 + bx + c, we will always notice that:

  • if a> 0, the parable has the upward facing;

  • if a <0, the parable has the downward facing;

Next: Zeros or Roots