What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for # y=x^210x+2#?
1 Answer

#y=x^210x+2# is the equation of a parabola which will open upwards(because of the positive coefficient of#x^2# )
So it will have a Minimum 
The Slope of this parabola is
#(dy)/(dx) = 2x10#
and this slope is equal to zero at the vertex
#2x  10 = 0#
#> 2x = 10 > x = 5# 
The X coordinate of the vertex will be
#5#
The vertex is at
and has a Minimum Value

The axis of symmetry is
#color(blue)(x=5# 
The domain will be
#color(blue)(inRR# (all real numbers) 
The range of this equation is
#color(blue)({y in RR : y>=23}# 
To get the x intercepts, we substitute y = 0
#x^210x+2 = 0#
We get two x intercepts as#color(blue)((5+sqrt23) and (5sqrt23)# 
To get the Y intercepts, we substitute x = 0
# y = 0^2 10*0 + 2 = 2#
We get the Y intercept as#color(blue)(2# 
This is how the Graph will look:
graph{x^210x+2 [52.03, 52.03, 26, 26]}