Radicals - Day 1

Today's lesson incorporated our graphic transformations (that we studied with the Quadratic and the Absolute Value function) with the square root function. The parent function looks like half of a parabola, turned on its side.

The generic form of the equation to graph a square root function is:

In this form, transformations are determined by:

• if the absolute value of a is greather than 1, then the graph is stretched taller;
  
• if the absolute value of a is between 0 and 1, then the graph is compressed shorter;
  
• if the value of a is less than 0, then the graph is reflected over the x-axis (flipped upside down);
  
• if the value of b is less than 0, then the graph is reflected over the y-axis (flipped over right to left);
  
• The value of h is always the opposite of whatever is "seen" within the square root (just like we did for the last 2 weeks) and this value shifts the graph to the left or right;
  
• The value of k is exactly whatever is "seen" after the square root (just like we did for the vertex form) and this value shift the graph up or down.

Students should always use a table of values to find points for their graphs. Pick x-values that will make the radicand (the inside of the square root) equal 0, equal 1, equal 4, and equal 9. We use these values because they are perfect square, so their square roots won't have us plotting decimal values for coordinates.

Example: Graph the following function:

• a = -2, so this graph will be flipped over and stretched taller by 2


• h = 1, so this graph will be shifted to the right 1 unit


• k = 4, so this graph will be shifted up 4 units


• use a table of to have points to graph: input x = -1, x = 2, x = 5, and x = 10.

Homework: Pages 140 & 141, #2 - 24 even

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