Let f(x)=x^2-4x+8
Find the number of points that lie on the graph of F at the indicated height y.

A) y=3
B y=4
C y=5

graph F and explain why the number of points to be 0, 1, 2 for parts b and c.

do I just set F(x) to each y and solve algebraically? book doesnt help much.

Question

Let f(x)=x^2-4x+8 
Find the number of points that lie on the graph of F at the indicated height y.

A) y=3
B y=4 
C y=5

graph F and explain why the number of points to be 0, 1, 2 for parts b and c.

do I just set F(x) to each y and solve algebraically? book doesnt help much.

asnaseer · Answer

yes, so for example for part A you would solve:$$3=x^2-4x+8$$$$x^2-4x+5=0$$solve this to find the roots. if the roots are NOT imaginary numbers, then this means that tat point lies on the graph.

anonymous · Answer

so from there i just use the quad. formula?

asnaseer · Answer

you can do, or you can use this method if you are familiar with it:$$x^2-4x+5=0$$$$(x-2)^2+1=0$$$$(x-2)^2=-1$$this implies imaginary roots.

anonymous · Answer

i dont know what that method is called. i use the quad formula and get 4 plus or minus root -4 over 10, so the root is a fraction. i know you arent supposed to have a minus in the root and that becomes i. 

but im stuck here. i dont understand how the author listed the solution as 0.

asnaseer · Answer

since you end up with the square root of a negative number, this implies that the point with y=3 does not lie on the graph.