The most important points should be the #color(red)"vertex"#, the #color(blue)("y-int")#, and the #color(green)"zeroes"# (if there are any).
The x-coordinate of the #color(red)(vertex)# of any quadratic equation
#y=ax^2+bx+c# is:
#(-b)/(2a)#
Plug in the x-coordinate back into the equation to find y. Do it on this equation:
#b=-6#
#a=1#
#c=1#
#(-(-6))/(2a)=3#
Now you have the #color(red)(vertex)# as #(3,y)#
#y=(3^2)-6*(3)+1=-8#
The #color(red)(vertex)# is #(3, -8)#
The #color(blue)("y-int")# of the quadratic equation
#y=ax^2+bx+color(orange)(c)# is simply #color(orange)(c)#.
The #color(blue)("y-int")# of this equation is #(0,1)#.
To find the #color(green)"zeroes"#, plug into the quadratic formula, which is given by:
#(-b+-sqrt(b^2-4ac))/(2a)#
Plug in:
#(6+-sqrt((-6)^2-4*1*1))/(2*1)#
Simplify:
#(6+-4sqrt(2))/2#
#3+-2sqrt(2)#
The #color(green)"zeroes"# are: #(5.828,0) and (0.172,0)#
