How do you graph y=-sqrt(4-x^2)?

1 Answer
Feb 29, 2016

Represents a semi circle, whose circumference lies below x-axis and which has origin (0,0) as its centre.

Explanation:

Plotted graph is as below.
graph{y=-sqrt(4-x^2) [-5, 5, -2.5, 2.5]}

Given expression is
y=-sqrt(4-x^2) ..........(1)
If we square both sides we obtain

y^2=4-x^2, rearranging we obtain

x^2+y^2=2^2.......(2)
It looks like an equation of a circle.
General equation of a circle whose center is at the point (h,k) and radius r is
(x-h)^2+(y-k)^2=r^2

So the equation (2) is of a circle which has radius r=2, and origin (0,0) as its center.
From the given expression we deduce that

  1. Equation (1) is a curve which has a properties as above. Also it must satisfy following two conditions.

  2. That y always has negative values due to the presence of -ve sign on the right hand side term.

  3. As square root of any negative number is imaginary and therefore, can not be plotted on a x,y graph. Implies that, argument of square root term must be positive.

Mathematically it can be written as
4-x^2>=0

Taking x to the left hand side and taking square root of both sides
we obtain x<=2

We see that the equation (1) represents a semi circle, whose circumference lies below x-axis and which has origin (0,0) as its center and radius r=2