How do you write #f(x) = x^2+3x-4# in vertex form?

1 Answer
Jim G.
Oct 9, 2017

#f(x)=(x+3/2)^2-25/4#

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"#

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

#• " ensure the coefficient of the "x^2" term is 1"#

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

#f(x)=x^2+3x-4larr" coefficient of "x^2" term is 1"#

#color(white)(f(x))=x^2+2(3/2)xcolor(red)(+9/4)color(red)(-9/4)-4#

#color(white)(f(x))=(x+3/2)^2-25/4larrcolor(red)" in vertex form"#

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