Question

What is the vertex of `y= (x-3)^2-2x^2-4x-9`?

Answer 1

`-5,25)`

Explanation:

`"first express in standard form "y=ax^2+bx+c color(white)(x);a!=0`

`"expand "(x-3)^2" using Foil and collect like terms"`

`y=x^2-6x+9-2x^2-4x-9`

`color(white)(y)=-x^2-10x`

`"the x-coordinate of the vertex is on the axis of"`
`"symmetry passing through the midpoint of the zeros"`

`"let y = 0"`

`rArr-x^2-10x=0`

`rArr-x(x+10)=0`

`rArrx=0,x=-10larrcolor(red)" are the zeros"`

`x_(color(red)"vertex")=(0-10)/2=-5`

`y_(color(red)"vertex")=-(-5)^2-10(-5)=25`

`rArrcolor(magenta)"vertex "=(-5,25)`