Question

What is the vertex of the parabola `y= -2(x+3)(x-1)`?

Answer 1

`"vertex "=(-1,8)`

Explanation:

`"the vertex lies on the axis of symmetry which is situated"`
`"at the midpoint of the zeros"`

`" to find zeros let y = 0"`

`rArr-2(x+3)(x-1)=0`

`"equate each factor to zero and solve for x"`

`x-1=0rArrx=1`

`x+3=0rArrx=-3`

`"axis of symmetry is "x=(1-3)/2=-1`

`"x-coordinate of vertex "=-1`

`"substitute "x=-1" into the equation for y-coordinate"`

`rArry=-2(2)(-2)=8`

`rArrcolor(magenta)"vertex "=(-1,8)`
graph{(y+2x^2+4x-6)((x+1)^2+(y-8)^2-0.04)=0 [-20, 20, -10, 10]}