Question

What is the vertex form of `y=(2x-9)(3x-1)`?

Answer 1

`y=6(x-29/24)^2-625/24`

Explanation:

Given -

`y=(2x-9)(3x-1)`

Vertex form of the equation is -

`y=a(x-h)^2+k`

Find the vertex first -

`y=6x^2-27x-2x+9`
`y=6x^2-29x+9`

x coordinate of the vertex
`x=(-b)/(2a)`

`x=(-(-29))/(2xx6)=29/12`

y-coordinate of the vertex

`y=6(29/12)^2-29(29/12)+9`
`y=6(841/144)-841/12+9`
`y=5046/144-841/12+9`
`y=(5046-10092+1296)/144=-3750/144=-625/24`
Vertex `(29/12, -625/24)`

`a=6` [coefficient of `x^2`]
`h=29/12` [x coordinae of the vertex]
`k=-625/24`

The vertex form of the parabola equation is -

`y=6(x-29/24)^2+((-625)/24)`
`y=6(x-29/24)^2-625/24`