What is the vertex form of $y = - 9 x^{2} + 12 x - 18$ $y=-9x^2 +12x - 18$ ?

Question

1912 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-26T01:53:47

Below is the proof (a completion of square)

$y = - 9 x^{2} + 12 x - 18$ $y = -9x^2 + 12x - 18$

$y = - 9 (x^{2} - \frac{12}{9} x) - 18$ $y = -9(x^2 - 12/9x) - 18$

$y = - 9 (x^{2} - \frac{12}{9} x +$ $y = -9(x^2 - 12/9x +$ _ - _ ) - 18#

$_= {(\frac{- \frac{12}{9}}{2})}^{2}$ $_ = ((-12/9) / 2)^2$

$_= \frac{4}{9}$ $_ = 4/9$

$y = - 9 (x^{2} - \frac{12}{9} x + \frac{4}{9}) - \frac{4}{9} (- 9) - 18$ $y = -9(x^2 - 12/9x + 4/9) - 4/9(-9) - 18$

$y = - 9 {(x - \frac{2}{3})}^{2} - 14$ $y= -9(x - 2/3)^2 - 14$

So, $y = - 9 x^{2} + 12 x - 18$ $y = -9x^2 + 12x - 18$ is equal to $y = - 9 {(x - \frac{2}{3})}^{2} - 14$ $y = -9(x - 2/3)^2 - 14$

Hopefully that explanation helped!

What is the vertex form of y=-9x^2 +12x - 18 y=−9x2+12x−18y=-9x^2 +12x - 18 ?