How do you write the quadratic function #y=3x^2-9x+18# in vertex form?

1 Answer
May 16, 2017

#y=3(x-3/2)^2+45/4#

Explanation:

#"the equation of a quadratic function 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.

#"rearrange " y=3x^2-9x+18" into this form"#

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

#" coefficient of " x^2" must be unity"#

#rArr3(x^2-3x)+18#

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

#"we must also subtract this value, since it is not"#
#"there to start with"#

#"that is add/subtract " (-3/2)^2=9/4#

#rArr3(x^2-3xcolor(red)(+9/4)color(red)(-9/4))+18#

#=3(x-3/2)^2-27/4+18#

#rArry=3(x-3/2)^2+45/4larrcolor(red)" in vertex form"#