1. Graphing Square Root Functions - 10. Radical Functions and Equations - Big Ideas Math Algebra 1 A Bridge to Success

A square root function is a function that has its independent variable in the radicand of a square root. We want to identify some of the characteristics of the graph of a square root function. Let's first draw the graph of the parent function y=sqrt(x).

Graph of the Parent Function

We will first find some points on the graph. Note that x must be a non-negative number because the value inside a square root cannot be negative. Therefore, we will randomly choose x=0, x=1, and x=4.

x	y=sqrt(x)	Point
0	sqrt(0)= 0	( 0, 0)
1	sqrt(1)= 1	( 1, 1)
4	sqrt(4)= 2	( 4, 2)

Great! Now, we can draw a smooth curve through these points.

As we can see, the graph starts from (0,0), increases quickly at first, and then slows its rate of increase. Since the inside of a square root cannot be negative, the domain of the parent function must be x ≥ 0. This means that the expression sqrt(x) produces only non-negative values. Therefore, the range of the function is y ≥ 0. Domain:& x ≥ 0 Range:& y ≥ 0

Graph of y=asqrt(x-h)+k

Now, we will examine those same characteristics for the general form of a square root function. y= asqrt(x- h)+ k Let's observe how the graph of the square root function changes when the variables a, h, and k change.

Here are some observations from the above graph.

The parent function stretches, shrinks, or reflects by the factor of a.
The parent function translates horizontally based on the value of h.
The parent function translates vertically based on the value of k.

Exercise 3 Page 543

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Graph of the Parent Function

Graph of y=asqrt(x-h)+k