How do you use the important points to sketch the graph of #y= x^2 - 4x#?

1 Answer
Feb 10, 2018

See explanation

Explanation:

#color(blue)("y intercept")#

#color(purple)(y_("intercept") " is when "x=0 => y_("intercept")=0)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("x intercept")#
#x_("intercept")" at "y=0 = x^2-4x#

Factor out #x# giving:

#color(purple)(y=0=x(x-4) =>x_("intercept")=0 and x_("intercept")=4)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("vertex")#

# x_("vertex")# is #1/2# way between x intercepts (mean value)

# color(purple)(x_("vertex") = (0+4)/2=2)#

To determine #y_("vertex")# substitute for #x#

# color(purple)(y_("vertex")=x^2-4x =(2)^2-4(2)=-4)#

# color(purple)("Vertex "->(x,y)=(2,-4)#

Tony B