How do you write the quadratic function #y=3x^2-9x+18# in vertex form?
1 Answer
May 16, 2017
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"#