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.
= 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.
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