Question

What is the vertex form of `y=-5/8x^2+7/4x +2/3`?

Answer 1

`y=-5/8(x-7/5)^2+227/120`

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"`

`•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=-5/8x^2+7/4x+2/3" is in standard form"`

`"with "a=-5/8,b=7/4" and "c=2/3`

`rArrx_(color(red)"vertex")=-(7/4)/(-5/4)=7/5`

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

`y_(color(red)"vertex")=-5/8(7/5)^2+7/4(7/5)+2/3=227/120`

`rArry=-5/8(x-7/5)^2+227/120larrcolor(blue)"in vertex form"`