Binomische Formel (Normalform)

Question

Aufgabe:

Führe die Funktionsgleichung in die Normalform über.

a) f (x)= (6-x)²

b) f(x)= (2x+5)²

c) f(x)= (7-x*3)²

Answer 1

f (x)= (6-x)^2=(6-x)*(6-x)=36-6x-6x+x^2=36-12x+x^2

f(x)= (2x+5)^2=(2x+5)*(2x+5)=4x^2+10x+10x+25=4x^2+20x+25

f(x)= (7-x*3)^2=(7-3x)^2=(7-3x)*(7-3x)=49-21x-21x+9x^2=49-42x+9x^2

binomische Normalform:

(a+b)^2=(a+b*(a+b)=a^2+ab+ba+b^2=a^2+2ab+b^2

(a-b)^2=(a-b)*(a-b)=a^2-ab-ba+b^2=a^2-2ab+b^2

Answer 2

Aloha :)

$$f(x)=(\underbrace{6}_{=a}-\underbrace{x}_{=b})^2=\underbrace{6^2}_{=a^2}-\underbrace{2\cdot6\cdot x}_{=2\cdot a\cdot b}+\underbrace{x^2}_{=b^2}=36-12x+x^2$$

$$f(x)=(\underbrace{2x}_{=a}+\underbrace{5}_{=b})^2=\underbrace{(2x)^2}_{=a^2}+\underbrace{2\cdot2x\cdot 5}_{=2\cdot a\cdot b}+\underbrace{5^2}_{=b^2}=4x^2+20x+25$$

$$f(x)=(\underbrace{7}_{=a}-\underbrace{3x}_{=b})^2=\underbrace{7^2}_{=a^2}-\underbrace{2\cdot7\cdot3x}_{=2\cdot a\cdot b}+\underbrace{(3x)^2}_{=b^2}=49-42x+9x^2$$