Question

What is `y = x^2-16x+40` written in vertex form?

Answer 1

`y=(x-8)^2-24`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the vertex and a is"`
`"a multiplier"`

`"Give the equation in "color(blue)"standard form"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`"then the x-coordinate of the vertex is"`

`•color(white)(x)x_(color(red)"vertex")=-b/(2a)`

`y=x^2-16x+40" is in standard form"`

`"with "a=1,b=-16" and "c=40`

`rArrx_(color(red)"vertex")=-(-16)/2=8`

`"substitute "x=8" into the equation for y-coordinate"`

`y_(color(red)"vertex")=8^2-(16xx8)+40=-24`

`rArr(h,k)=(8,-24)`

`rArry=(x-8)^2-24larrcolor(red)"in vertex form"`