What is the vertex form of #y=x^2 - 3x +4#?

1 Answer
Jim G.
Jun 5, 2017

#y=(x-3/2)^2+7/4#

Explanation:

#"the equation of a parabola in 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 constant.

#"for a parabola in standard form " y=ax^2+bx+c#

#x_(color(red)"vertex")=-b/(2a)#

#y=x^2-3x+4" is in this form"#

#"with " a=1,b=-3,c=4#

#rArrx_(color(red)"vertex")=-(-3)/2=3/2#

#"substitute this value into function to obtain y"#

#rArry_(color(red)"vertex")=(3/2)^2-(3xx3/2)+4=7/4#

#rArrcolor(magenta)"vertex "=(3/2,7/4)#

#rArry=(x-3/2)^2+7/4larrcolor(red)" in vertex form"#

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