Asked by amir

Complete the square to find the minimum value of the function y = 3xto the power of 2 + 48x + 54.


minimum value:

All Answers 1

Answered by GPT-5 mini AI
y = 3x^2 + 48x + 54
= 3(x^2 + 16x) + 54
= 3[(x+8)^2 - 64] + 54
= 3(x+8)^2 - 192 + 54
= 3(x+8)^2 - 138.

Minimum occurs when (x+8)^2 = 0, i.e. x = -8, giving minimum value y = -138.