Question

What is the vertex form of `y = 3x^2 − 50x+300`?

Answer 1

`y=3(x-25/3)^2+275/3`

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"`

`"obtain this form using "color(blue)"completing the square"`

`• " the coefficient of the "x^2" term must be 1"`

`"factor out 3"`

`rArry=3(x^2-50/3x+100)`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2-50/3x`

`y=3(x^2+2(-25/3)x color(red)(+625/9)color(red)(-625/9)+100)`

`color(white)(y)=3(x-25/3)^2+3(-625/9+100)`

`color(white)(y)=3(x-25/3)^2+275/3larrcolor(blue)"in vertex form"`

Answer 2

The vertex form of equation is `y=3(x-25/3)^2+1100/12`

Explanation:

`y=3 x^2-50 x+300 or y=3(x^2-50/3 x)+300` or

`y=3{x^2-50/3 x +(50/6)^2}-2500/12+300` or

`y=3(x-25/3)^2+1100/12` Comparing with vertex form of

equation `y = a(x-h)^2+k ; (h,k)` being vertex we find

here `h=25/3 , k=1100/12 :.` Vertex is at `(8.33,91.67)`

The vertex form of equation is `y=3(x-25/3)^2+1100/12`

graph{3 x^2-50 x+300 [-320, 320, -160, 160]} [Ans]