Completing the Square - Multiple Variables Practice Problems Online

For real numbers $x$ , $y$ and $z$ , function $f(x,y,z)=4x-x^2-y^2-z^2+18$ has a maximum value $d$ at $x=a$ , $y=b$ and $z=c$ . What is the value of $a+b+c+d$ ?

For real numbers $x$ , $y$ and $z$ , function $f(x,y,z)=x^2+y^2+z^2-4x-4y-4z+14$ has a minimum value $d$ at $x=a$ , $y=b$ and $z=c$ . What is the value of $a+b+c+d$ ?

For real numbers $x$ and $y$ , function $f(x,y)=x^2+2y^2-4x-16y+21$ has a minimum value $c$ at $x=a$ and $y=b$ . What is the value of $a+b-c$ ?

For real numbers $x$ and $y$ , function $f(x,y)=2x-x^2+2y-y^2+28$ has a maximum value $c$ at $x=a$ and $y=b$ . What is the value of $a+b+c$ ?

What is the maximum value of $f(f(x))$ in the domain $2 \leq x \leq 5$ for the function $f(x)=x^2-6x+4?$

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Completing the Square - Multiple Variables

Completing The Square Generalized

Concept Quizzes

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Completing the Square - Multiple Variables