10.5 Graphing Square Root Functions Algebra I

First, let’s look at the parent graphs.

Now, what happens when there is a number in front of the radical? * Notice the graph goes thru the points (0,0) and (1,2).

Generalization Always goes thru the points (0,0) and (1,a).

Ex. 1: Graph Goes thru the points (0,0) and (1,a). Since a=-4, the graph will pass thru (0,0) and (1,-4)

Now, what happens when there are numbers added or subtracted inside and/or outside the radical? Step 1: Find points on the parent graph Step 2: Shift these points h units horizontally (use opposite sign) and k units vertically (use same sign) or use t-chart to figure out 2 new points.

Ex. 2: Describe how to obtain the graph of from the graph of Shift all the points from To the right 2 and up 1.

Ex. 3: Graph Now, shift these points to the left 4 and down 1. x y 0 0 (x-value – 4) (y-value -1) Now, shift these points to the left 4 and down 1. x y 0 0 2 4 9 6 x y -4 -1 -3 1 0 3 5 5

Ex. 3 & 4: State the domain and range of the functions in the last example. x-values Domain: Range: The graph has a beginning point of (-4,-1).

Assignment