Square root graph: y = √x

Updated 20 October 2026 · Values computed by the ihateDesmos engine

The square root graph starts at the origin and curves to the right, rising quickly at first and then more and more slowly. It is the top half of the parabola x = y², lying on its side.

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The graph of

y=√x

for −2 ≤ x ≤ 12. Dots mark its starting point.

Key features

Domain: x ≥ 0
Range: y ≥ 0
Starting point: (0, 0), where the tangent is vertical
Perfect-square points: (1, 1), (4, 2), (9, 3), (16, 4)
Monotonic: Increasing
Concavity: Concave down
y-intercept: (0, 0)
Derivative: 12√x
Antiderivative: 2x³²3+C

Derivative and antiderivative from the calculator’s algebra system. Domain, range and asymptotes are stated for real x.

What the graph of √x looks like

Only non-negative numbers have real square roots, so the graph begins at x = 0 and goes right. The symbol √ means the principal (non-negative) root, so the graph never dips below the x-axis.

Squaring and square-rooting undo each other, so √x is the right half of the parabola y = x², reflected in the line y = x. That reflection turns the flat bottom of the parabola into a vertical tangent at the origin.

The perfect squares make the curvature easy to see: to rise from 1 to 2 the graph needs 3 units of x, from 2 to 3 it needs 5, from 3 to 4 it needs 7.

Points of interest

Found numerically to about twelve digits in the window −2 ≤ x ≤ 12, then shown in exact form where one exists.

x-intercepts (roots): None in this window
Local maxima: None in this window
Local minima: None in this window
Inflection points: None in this window

Table of values

A few points to plot, with exact values where they are simple.

Values of √x
x	y = √x
0	0
1/4	1/2
1	1
2	√2
4	2
9	3
16	4

How to graph √x by hand

1
Plot (0, 0), (1, 1), (4, 2) and (9, 3).
2
Start the curve vertically at the origin and bend it to the right through the other points.
3
Do not extend it to the left of the y-axis or below the x-axis.

Transformations

How the graph moves when you change the formula. The original is √x in blue.

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y = sqrt(x + 2) Shifted left 2: the domain becomes x ≥ −2.
y = -sqrt(x) Reflected in the x-axis: the bottom half of the sideways parabola.
y = sqrt(-x) Reflected in the y-axis: domain x ≤ 0.