Question

What is the vertex form of `y= 4x^2 -12x + 9`?

Answer 1

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

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 constant.

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

`"the x-coordinate of the vertex is " x_(color(red)"vertex")=-b/(2a)`

`y=4x^2-12x+9" is in standard form"`

`"with " a=4,b=-12,c=9`

`rArrx_(color(red)"vertex")=-(-12)/8=3/2`

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

`y=4(3/2)^2-12(3/2)+9=9-18+9=0`

`rArrcolor(magenta)"vertex " =(3/2,0)`

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