Question

What is the vertex form of `y=4/5x^2-3/8x+3/8`?

Answer 1

`y=(x-15/64)^2+339/1024`

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=4/5x^2-3/8x+3/8" is in standard form"`

`"with "a=4/5,b=-3/8 and "c=3/8`

`rArrx_(color(red)"vertex")=-(-3/8)/(8/5)=15/64`

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

`y=4/5(15/64)^2-3/8(15/64)+3/8=339/1024`

`rArry=(x-15/64)^2+339/1024larrcolor(red)"in vertex form"`