What is Y a bx

Drawing quadratic functions and parabolas

In this section we will deal with what are known as quadratic functions and how to plot them. First of all, we will show you what this type of function is all about. Then we go into the sign of this.

A quadratic function is a function that has the following form: f (x) = ax2 + bx + c with a not equal to zero. Often the equation y = ax2 + bx + c used. A, b and c are arbitrary numbers, whereby a, as already described, must be non-zero. The following examples demonstrate this:

  • y = 5x2 + 3x + 5
  • y = 2x2 + 2x + 8
  • y = 4x2 + 2
  • y = 2x2
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Quadratic function: parabola

Let's start with a quadratic function that is particularly simple: a parabola. This has the form f (x) = y = x, for example2 and should be drawn in the following. For all those who cannot imagine a table of values ​​or a coordinate system, the article linear functions is available (opens in new browser window).

This is how quadratic functions and parabolas are drawn:

  • First create the table of values. As always, numbers are used for x and thus y is calculated.
  • Make the crosses at the intersections x-y to mark the intersection points.
  • The points are connected. However, we do not have a linear relationship here. Therefore, you are not allowed to draw a straight line, but rather "anticipate" the course. If you still have problems with this, you should not only use numbers such as 1, 2, 3 for x, but also decimal numbers / point numbers (1,2 or 1,3 etc.) to find more points.
  • The function of course continues upwards, even if no additional points are entered.
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Quadratic function: example 2

The parable we just looked at was still pretty simple. For a better understanding, let's now draw a somewhat more complicated function. For this we take the function f (x) = y = -0.5x2 + 3 in front. Here, too, we create a table of values ​​and use this to plot the function in an x-y coordinate system.

Note: The procedure is always the same: table of values, drawing in points and connecting points. The unpleasant thing about this function is the sign when a negative number is used. Here is an example of the first invoice:

  • y = -0.5 (-3)2 + 3 = -0,5 · 9 + 3 = -4,5 + 3 = -1,5.

In order to get fit in drawing quadratic functions, I advise you to carry out our exercises and tasks on the topic yourself.

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