Multiple choice

Arrange the following quadratic expressions in the ascending order of their extreme values $\displaystyle {A}:\frac{11}{3}-\left(x-\frac{3}{5}\right)^{2}$ ${B}:{x}^{2}-8{x}+17$ ${C}:{x}^{2}+6{x}-27$ ${D}:15+4{x}-3{x}^{2}$

  1. ${A},{B},{C}, {D}$
  2. $ B,A,{C}, {D}$
  3. $ {C}, B,A, {D}$
  4. $ {A},{B},{D},{C}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Find the extreme values (max or min): A is 11/3 (max), B is (x-4)^2 + 1, so min is 1. C is (x+3)^2 - 36, so min is -36. D is -3(x^2 - 4/3x) + 15 = -3(x-2/3)^2 + 15 + 4/3 = 16.33 (max). Ascending order of these values (-36, 1, 3.66, 16.33) corresponds to C, B, A, D.

AI explanation

The extreme value of A is 11/3, B has a minimum of 1, C has a minimum of -36, and D has a maximum of 49/3. The problem asks for the ascending order of these extreme values. Since -36 < 1 < 11/3 < 49/3, the correct ascending order of the expressions by their extreme values is C, B, A, D.

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