What is the vertex form of $y= 3x^2-30x-72$ ?

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Answer 1 · 2016-03-27T20:01:49

$y=3(x-5)^2 -147$

Given: $" "y=3x^2-30x-72$

Let $k$ be the correction canstant

Write as; $" "y=3(x^(color(magenta)(2))-30/3x)-72+k$

Move the power of $color(magenta)(2)$ to outside the bracket

$y=3(x-30/3color(green)(x))^(color(magenta)(2))-72+k$

Remove the $color(green)(x)$ from $30/3x$

$y=3(x-30/3)^2 -72+k$

Apply $1/2xx(-30/3) = 30/6 = 5$

$y=3(x-5)^2 -72+k$

For the correction to work it has to be the case that

$color(red)(3)xx(-5)^2+k=0" "=>" "k=-75$

$color(red)("(do not forget to multiply by the value outside the brackets)")$

$y=3(x-5)^2 -72-75$

$y=3(x-5)^2 -147$

What is the vertex form of y= 3x^2-30x-72 y= 3x^2-30x-72 ?