Question

What is the vertex form of `y=x^2 - 3x +4`?

Answer 1

`y=(x-3/2)^2+7/4`

Explanation:

`"the equation of a parabola in 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 constant.

`"for a parabola in standard form " y=ax^2+bx+c`

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

`y=x^2-3x+4" is in this form"`

`"with " a=1,b=-3,c=4`

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

`"substitute this value into function to obtain y"`

`rArry_(color(red)"vertex")=(3/2)^2-(3xx3/2)+4=7/4`

`rArrcolor(magenta)"vertex "=(3/2,7/4)`

`rArry=(x-3/2)^2+7/4larrcolor(red)" in vertex form"`