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)