Question

How do you write the quadratic in vertex form given `y=-4x^2+12x+5`?

Answer 1

`y=-4(x-3/2)^2+14`

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"`

`"to obtain this form use the method of "color(blue)"completing the square"`

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

`"factor out "-4`

`y=-4(x^2-3x-5/4)`

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

`y=-4(x^2+2(-3/2)x color(red)(+9/4)color(red)(-9/4)-5/4)`

`color(white)(y)=-4(x-3/2)^2-4(-9/4-5/4)`

`color(white)(y)=-4(x-3/2)^2+14larrcolor(red)"in vertex form"`