Core 1 graphs question

How would I find the minimum value of the graph for (3x^2 -12x +5)^2?

Original post by francescan

How would I find the minimum value of the graph for (3x^2 -12x +5)^2?

complete the square

Original post by 123Master321

complete the square

Would it be correct to complete the square as (3(x-2)^2 -7)^2 ? This would mean the minimum value is (2,49) which isn't right

(edited 7 years ago)

Original post by 123Master321

[br](3x^2-12x+5)^2[br]=(3(x^2-4x))+5[br]=3((x-2)^2-4)+5[br]=(3(x-2)^2-7)^2[br]

Now, the minimum of this is not when the inner square bit is zero more when the bit inside the outer square bit is zero, namely

[br]3(x-2)^2-7=0[br]x=2 \pm \sqrt{\frac{7}{3}}[br]

which gives y=0

Ahhh that makes more sense, thank you so much!!

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