How would I convert this equation to standard form? y = -2 (x - 6)^2 + 8

Shadew
Dec 15, 2014

#1**+10 **

Best Answer

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

y=-2(x^2-12x+36)+8\\

y=-2x^2+24x-72+8\\

y=-2x^2+24x-64\\$$

Melody
Dec 15, 2014

#3**+5 **

Hi shadew,

Sorry I took so long to get back to you I have been busy today.

I am very glad that you asked - I like to get feed back :)

This is the long way I could have done $$(x-6)^2$$

$$\\(x-6)^2\\

=(x-6)(x-6)\\

=x(x-6)\;\;-6(x+6)\\

=x^2-6x\;\;-6x-36\\

=x^2-12x+36$$

Now $$(x-6)^2$$ is a perfect square. There is a short cut method.

$$\\(a\pm b)^2=a^2\;\pm\;(2*a*b)\;+\;b^2\\

so\\

(x-6)^2=x^2\;-\;(2*x*6)\;+\;6^2=x^2-12x+36$$

I sometimes use this method when I want to square numbers in my head

eg

$$\\23^2\\

=(20+3)^2\\

=20^2+(2*20*3)+3^2\\

=400+120+9\\

=529$$

Melody
Dec 16, 2014