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

##### 1 Answer

Oct 11, 2017

#### 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"#