Multiple choice general knowledge math & puzzles

What is the least possible value of the function f(x,y). Given f(x,y)= 2x^2+3y^2+8x+24y+80

  1. 56

  2. 40

  3. 24

  4. 32
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Complete the square: f(x,y) = 2(x^2+4x) + 3(y^2+8y) + 80 = 2[(x+2)^2 - 4] + 3[(y+4)^2 - 16] + 80 = 2(x+2)^2 + 3(y+4)^2 - 8 - 48 + 80 = 2(x+2)^2 + 3(y+4)^2 + 24. Minimum is 24 when x=-2, y=-4.

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