y=-x^2 + 2x + 8
What is the range

Question

y=-x^2 + 2x + 8
What is the range

anonymous · Answer

you need help?

anonymous · Answer

the range is set of values that y can assume given a value of x.  if we think about this by first picturing the graph in our head.. that would be best.

anonymous · Answer

I wanted to know the math steps to do it

amoodarya · Answer

y=-x^2 + 2x + 8
y=-(x^2 - 2x) + 8
y=-((x-1)^2-1)) + 8
y=-(x-1)^2+1+8
y=-(x-1)^2+9

now 
y-9=-(x-1)^2
9-y=(x-1)^2 >=0

so 9-y>=0

so 
y<=9

anonymous · Answer

ok sorry.  i just find it easier to think of this as the graph of -x^2 shifted up by 8 units and right by 1.

amoodarya · Answer

"Nameless" it is wrong because by shifting +1 right and shif +8 range became y<8 but another method is using discriminant x^2-2x-8+y=0 delta >=0 4-4(-8+y)>=0 1+8 -y>=0 y<=9

anonymous · Answer

ahh i totally overlooked that.  nice.

anonymous · Answer

THANK YOU!

anonymous · Answer

amoodarya can you please explain were you got the 4-4 in front of (-8+y)