How do you write #f(x) = x^2+7x+10# in vertex form?

1 Answer
Aug 6, 2017

#y=(x+7/2)^2-9/4#

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 constant.

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

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

#y=x^2+7x+10" is in standard form"#

#"with "a=1,b=7,c=10#

#rArrx_(color(red)"vertex")=-7/2#

#"substitute this value into f(x) for y-coordinate"#

#y_(color(red)"vertex")=(-7/2)^2+(7xx-7/2)+10=-9/4#

#rArrcolor(magenta)"vertex "=(-7/2,-9/4)#

#rArry=(x+7/2)^2-9/4larrcolor(red)" in vertex form"#