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

##### 1 Answer

Oct 3, 2017

#### 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)#