How do you find the domain and range of #y=2x^2-4x+3#?
2 Answers
Range:
Domain:
Explanation:
the domain is "all x" (
in order to find the range of the function, giving that it is "a smiling parabola" (
now find
so the min is
Explanation:
#"this is a polynomial of degree 2 and is defined for all real"#
#"values of "x#
#"domain is "x inRR#
#"to find the range we require the vertex and whether it is"#
#"a maximum or minimum turning point"#
#"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"#
#"to obtain this form use "color(blue)"completing the square"#
#y=2(x^2-2x+3/2)#
#color(white)(y)=2(x^2+2(-1)x color(red)(+1)color(red)(-1)+3/2)#
#color(white)(y)=2(x-1)^2+1larrcolor(blue)"in vertex form"#
#color(magenta)" vertex "=(1,1)#
#"Since "a>0" then minimum turning point " uuu#
#"range is "y in[1,oo)#
graph{2x^2-4x+3 [-10, 10, -5, 5]}