Question

Solve the equation by graphing.

5 = -√x-3

I don't know how to make the graph. What would the graph look like? I worked out the equation and this is what it came out to be: 5 ≠ -5, which is no solution. Is there a way to graph this? Sorry, confused... please help.

Answer 1

Since the domain of √x is x>=0, you will need (x-3) >= 0. That is, x >= 3.

So, plug in some values of x and plot the points for y=-√(x-3):

x y
3 0
4 -1
7 -2
12 -3
...

It will look like the bottom half of a horizontal parabola with vertex at (3,0). The equation could also be written as

y^2 = x-3
x = y^2+3

However, your "no solution" answer is correct. √(x-3) is always positive, so -√(x-3) can never be 5.