Question

What is the vertex form of `6y=(x + 13)(x - 3)`?

Answer 1

`y=1/6(x+5)^2-32/3`

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"`

`6y=(x+13)(x-3)=x^2+10x-39`

`rArry=1/6(x^2+10x-39)`

`"using the method of "color(blue)"completing the square"`

`"on "x^2+10x-39`

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

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2+10x`

`x^2+2(5)xcolor(red)(+25)color(red)(-25)-39=(x+5)^2-64`

`rArry=1/6(x+5)^2-32/3`