What is the vertex form of #y= 3x^2-10x-14#?
1 Answer
May 29, 2017
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 " ax^2+bx+c#
#x_(color(red)"vertex")=-b/(2a)#
#y=3x^2-10x-14" is in this form"#
#"with " a=3,b=-10,c=-14#
#rArrx_(color(red)"vertex")=-(-10)/6=5/3#
#"for y-coordinate, substitute this value into the equation"#
#rArry_(color(red)"vertex")=3(5/3)^2-10(5/3)-14=-67/3#
#rArrcolor(magenta)"vertex "=(5/3,-67/3)#
#rArry=3(x-5/3)^2-67/3larrcolor(red)" in vertex form"#
