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]}