Question

What is the vertex form of `y=x^2-7x+1`?

Answer 1

`y=(x-7/2)^2-45/4`

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"`

`"given the equation in standard form ";ax^2+bx+c`

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

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

`y=x^2-7x+1" is in standard form"`

`"with "a=1,b=-7" and "c=1`

`rArrx_(color(red)"vertex")=-(-7)/2=7/2`

`"substitute this value into the equation for y"`

`y_(color(red)"vertex")=(7/2)^2-7(7/2)+1=-45/4`

`rArry=(x-7/2)^2-45/4larrcolor(red)"in vertex form"`