What is the vertex form of $y = 6x^2 - 24x + 16$ ?

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Answer 1 · 2018-07-08T17:49:44

$y=6(x-2)^2-8$

We have

$y=6x^2-24x+16$
and this is

$y=6(x^2-4x+16/6)$
$y=6(x^2-4x+8/3)$
now we complete the square

$y=6(x^2-4x+4+8/3-4)$

we use that

$x^2-4x+4=(x-2)^2$
and

$8/3-4=8/3-12/3=-4/3$

so we get

$y=6(x-2)^2-6*4/3$

the result is given by

$y=6(x-2)^2-8$
and this is the vertex form

What is the vertex form of y = 6x^2 - 24x + 16y = 6x^2 - 24x + 16?