Funktioner

Here are formulas and regulations, which can be used for functions.

Important!! GeoGebra distinguishes between equations and functions. If you want to use different commands to functions, then you into the input field type only the part of the regulation, which is after the equal sign. Write 2x + 3, although there are y = 2x + 3.

First Grade Function

Regulations

Regulations for first degree function (a straight line)

\(f(x)\) = \(a) • x + \(b)

The value \(a) called the slope or gradient century. The value in place of \(a) says something about, how much the line rises or falls. If \(a) he positively, so is the bar rising. If \(a) it is negative, so is the bar decreasing.

The value \(b) says, where the line crosses the y-axis (the lodrett).

Fx then graph the line f(x) = 2x + 3 be drawn through 3 y-axis (Ie. through point (0,3) ) and increase (slope) with 2.

Signs

For example, to sign the GeoGebra, you shall in the input field to write

2x + 3

Spirit Level Function

Regulations

Regulations for a spirit level function (in parabel)

\(f(x)\) = \(a) • x(^2) + \(b) • x + \(c)

Roots and peaks

You can find any roots(Rhodium) (points of intersection of the X axis) and vertex (extreme) using. the following commands in the input field

Rhodium[f]
Extreme[f]

Signs

For example if you want the sign function \(f(x)\) = 2 x(^2) + 3 x – 4 , so you just need to type the following into the input field

2*x ^ 2 + 3*x - 4

Diskriminanten

Discriminant says something about, the number of roots(points of intersection of the X axis) graph has. Discriminant counted out using. a formal, that Hedda

D = \(b^2) – 4 • \(a) • \(c)

1. If D < 0 (less than 0) skærer parablens ‘ben’ NOT X-axis (NO SOLUTION TO THE EQUATION)
2. If D = 0 (equal to 0) skærer parablens ‘ben’ X-axis ONE place. (Solving x =-b /(2a))
3. If D > 0 (greater than 0) skærer parablens ‘ben’ X-axis TO places.

The solutions s₁ = (-b √ D)/(2a) og S₂ = (-b-√ D)/(2a)

Info om a-,b- and c-values

Below is a little info about, what a, b and c values ​​say about the graph of the function.

a is the slope of the

1. Hvis a er negativ vender parablens ‘ben’ nedad. (sur Smiley)
2. Hvis a er positiv vender parablens ‘ben’ opad. (glad smiley)
3. The greater a, desto smallers parabel
4. The smaller a, desto Bredero parabel

b says something about, wherein the parabola is located relative to the y-axis.

1. If b = 0, so the parabola apex is located on the y-axis.
2. If a and b have the same sign, so the apex is located to the left of the y-axis.
3. If a and b have different signs, so the apex is located to the right of the y-axis.

c is the parabola intersection with the y-axis.

1. If c = 0, then goes through the point of the parabola (0,0)