+386 f(x) = 4- sqrt (16 + 6x - x^2)
I think I have problems with the input of the graph writer provided by web2.0calc.
It gives me an "f" with finite ends.
By the way, I don't understand how to link an image of the graph to a forum post.
I also need to find it's domain and image and it's intersection points with x=0 or y=0.
+23252 f(x) = 4 - sqrt(16 + 6x - x2)
For ease of calculation, I am replacing f(x) with y:
y = 4 - sqrt(16 + 6x - x2)
Subtract 4 from both sides: y - 4 = - sqrt(16 + 6x - x2)
Multiply both sides by -1: -y + 4 = sqrt(16 + 6x - x2)
Simplify left side: 4 - y = sqrt(16 + 6x - x2)
Square both sides: (4 - y)2 = 16 + 6x - x2
Multiply out: 16 - 8y + y2 = 16 + 6x - x2
Subtract 16 from both sides: - 8y + y2 = 6x - x2
Rewrite: y2 - 8y = -x2 + 6x
Factor: y2 - 8y = -(x2 - 6x)
Complete the squares: [ y2 - 8y + 16 ] - 16 = [ -(x2 - 6x + 9) ] + 9
Simplify: [ y2 - 8y + 16 ] = [ -(x2 - 6x + 9) ] + 25
Factor: (y + 4)2 = -(x - 3)2 + 25
Rewrite: (x - 3)2 + (y + 4)2 = 25
Analysis: this is the equation of a circle with center (3, -4) and radius = 5.
But: the initial equation is only the lower half of this circle; thus, an arc from (-2,4) through (3,-1) to 8,4).
+386 Thanks a lot for your help!
Could you explain to me that "complete the squares" part?
I don't get why there's suddenly a +16 and -16 on one side and a two time +9 on the other.
Thanks!
