Question

Thanks for your help . I need to sketch the graph of
f(x) = Sqrt 5-4x-x2 by completing the square. I assume I use the quadratic formula for this. But I am a little confused.

Answer 1

I am going to guess that you mean

fx) = √(5-4x-x^2) or y = √(5-4x-x^2)

square both sides
y^2 = 5-4x - x^2

x^2 + 4x + y^2 = 5
x^2 + 4x + <b>4</b> + y^2 = 5 + <b>4</b>
(x+2)^2 + y^2 = 9

you should recognize this as a circle with centre at (-2,0) and radius of 3

but we squared the original equation, so your graph would only be the part of the circle which is on and above the x-axis