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  3. Chapter 3: Functions of two variables
  4. List of functions of two variables
  5. Polynomial functions
  6. Quadratic functions
  7. Exercise

Exercise

Which of the following functions is a quadratic function of two variables, and what is the function value in (x,y)=(1,2)?
y(x)=−x2+5x−3; the corresponding function value is 6.
z(x,y)=x3+xy+y2−3x−5y+7; the corresponding function value is 1.
z(x,y)=(x+y)2−3; the corresponding function value is 6.
z(x,y)=(x+y)2−3; the corresponding function value is (1,2).
Which of the following functions is a quadratic function of two variables, and what is the function value in (x,y)=(1,2)?
Antwoord 1 correct
Fout
Antwoord 2 optie
z(x,y)=(x+y)2−3; the corresponding function value is (1,2).
Antwoord 2 correct
Fout
Antwoord 3 optie
z(x,y)=(x+y)2−3; the corresponding function value is 6.
Antwoord 3 correct
Correct
Antwoord 4 optie
y(x)=−x2+5x−3; the corresponding function value is 6.
Antwoord 4 correct
Fout
Antwoord 1 optie
z(x,y)=x3+xy+y2−3x−5y+7; the corresponding function value is 1.
Antwoord 1 feedback
Wrong: Although z(1,2)=1, z(x,y)=x3+xy+y2−3x−5y+7 is not a quadratic function.

See Quadratic function of two variables.
Antwoord 2 feedback
Wrong: z(x,y)=(x+y)2−3 is indeed a quadratic function of two variables, but the function value is the value of the output variable, not of the input variables.

See Functions of two variables.
Antwoord 3 feedback
Correct: z(x,y)=(x+y)2−3=x2+2xy+y2−3 is indeed a quadratic function of two variables. The function value is z(1,2)=(1+2)2−3=6.

Go on.
Antwoord 4 feedback
Wrong: y(x)=−x2+5x+2 is a quadratic function of one variable, not of two.

See Quadratic functions of two variables.