What is the vertex form of #y= x^2-3x-1 #?
1 Answer
Oct 3, 2017
Explanation:
#"the equation of a parabola in "color(blue)"vertex form"# is.
#•color(white)(x)y=a(x-h)^2+k#
#"where "(h,k)" are the coordinates of the vertex and a is a"#
#"multiplier"#
#"given the parabola in standard form "#
#•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0#
#"then the x-coordinate of the vertex is"#
#•color(white)(x)x_(color(red)"vertex")=-b/(2a)#
#y=x^2-3x-1" is in standard form"#
#"with "a=1,b=-3,c=-1#
#rArrx_(color(red)"vertex")=-(-3)/2=3/2#
#"substitute this value into y for y-coordinate"#
#y_(color(red)"vertex")=(3/2)^2-3(3/2)-1=-13/4#
#rArr(h,k)=(3/2,-13/4)#
#rArry=(x-3/2)^2-13/4larrcolor(red)" in vertex form"#
