Question

What is the vertex form of `y= x^2-3x-1`?

Answer 1

`y=(x-3/2)^2-13/4`

Explanation:

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

`•color(white)(x)y=a(x-h)^2+k`

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

`"given the parabola in 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^2-3x-1" is in standard form"`

`"with "a=1,b=-3,c=-1`

`rArrx_(color(red)"vertex")=-(-3)/2=3/2`

`"substitute this value into y for y-coordinate"`

`y_(color(red)"vertex")=(3/2)^2-3(3/2)-1=-13/4`

`rArr(h,k)=(3/2,-13/4)`

`rArry=(x-3/2)^2-13/4larrcolor(red)" in vertex form"`