Question

How do you write the vertex form equation of the parabola `2x² - 4x + y + 5 = 0`?

Answer 1

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

Explanation:

`"rearrange the equation making y the subject"`

`rArry=-2x^2+4x-5`

`"the equation of the 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"`

`"to express "y=-2x^2+4x-5" in this form"`

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

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

`rArry=-2(x^2-2x)-5`

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

`y=-2(x^2+2(-1)xcolor(red)(+1)color(red)(-1))-5`

`color(white)(y)=-2(x-1)^2+2-5`

`rArry=-2(x-1)^2-3larrcolor(red)" in vertex form"`