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How do you graph y = √ 5 - x? How do I find the coordinates by hand?

User Dalbergia
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1 Answer

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Each point is of the form (x,y). We replace x with some number to get a paired y value.

For instance, if x = 1, then,


y = √(5-x)\\\\y = √(5-1)\\\\y = √(4)\\\\y = 2

Meaning x = 1 and y = 2 pair up. The point (x,y) = (1,2) is on the curve.

Then let's try x = 4


y = √(5-x)\\\\y = √(5-4)\\\\y = √(1)\\\\y = 1

Showing (4,1) is also on the curve.

The point (5,0) is also on the curve too because of the steps below


y = √(5-x)\\\\y = √(5-5)\\\\y = √(0)\\\\y = 0

We can't go any higher than x = 5 or else the expression 5-x will be negative. Eg: if x = 7, then 5-x = 5-7 = -2. We cannot take the square root of a negative and get some real number output.

So let's go in the opposite direction. Let's try x = -4


y = √(5-x)\\\\y = √(5-(-4))\\\\y=√(5+4)\\\\y = √(9)\\\\y = 3

Showing (-4,3) is also on the curve.

The x values I'm picking are such that the y value is an integer. For the majority of the x values, you'll get some decimal value which is a bit tricky to graph on paper. So effectively you'll have to use trial and error to find the right x values to pick. The goal is to get the stuff under the square root to simplify to some perfect square (0,1,4,9,...etc)

After generating enough points, you draw a curve through them all. The more points, the more accurate the graph.

User CaldasGSM
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5.1k points