1. Home
  2. For business economics
  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 $(x,y)=(1,2)$?
$z(x,y) = x^3 +xy + y^2 - 3x -5y + 7$; the corresponding function value is 1.
$z(x,y) = (x+y)^2-3$; the corresponding function value is $(1,2)$.
$z(x,y) = (x+y)^2-3$; the corresponding function value is 6.
$y(x) = -x^2 + 5x-3$; the corresponding function value is 6.
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
$y(x) = -x^2 + 5x-3$; the corresponding function value is 6.
Antwoord 4 correct
Fout
Antwoord 1 optie
$z(x,y) = x^3 +xy + y^2 - 3x -5y + 7$; the corresponding function value is 1.
Antwoord 1 feedback
Wrong: Although $z(1,2)=1$, $z(x,y) = x^3 +xy + y^2 - 3x -5y + 7$ 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: $z(x,y)=(x+y)^2-3 = x^2 + 2xy +y^2 -3$ 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: $y(x)=-x^2 + 5x+2$ is a quadratic function of one variable, not of two.

See Quadratic functions of two variables.