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## ashking1 one year ago Find the vertex of the graph of the function. f(x) = 3x^2 - 24x + 51 can someone help me understand vertex and how to solve for it please

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1. SolomonZelman

$$\large { \displaystyle{\rm f}(x) = 3x^2 - 24x + 51}$$ $$\large { \displaystyle{\rm f}(x) = 3(x^2 - 8x) + 51}$$ $$\large { \displaystyle{\rm f}(x) = 3(x^2 - 8x\color{blue}{+16}\color{red}{-16}) + 51}$$ $$\large { \displaystyle{\rm f}(x) = 3(x^2 - 8x\color{blue}{+16})+3(\color{red}{-16}) + 51}$$ $$\large { \displaystyle{\rm f}(x) = 3(x-4)(x-4)-48 + 51}$$ $$\large { \displaystyle{\rm f}(x) = 3(x-4)^2+3}$$

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