Transforming Square Root Functions EQ What other relationships

Transforming Square Root Functions

EQ: What other relationships can we model? � Work ---

Transforming Square Root Functions Objective DOL �SWBAT graph, �Given 2 CR problems, transform, and interpret square root functions. �(CCSS. HSA. REI. B. 4) SW graph, transform, and interpret square root functions with 80% accuracy. EQ: What other relationships can we model?

Why? Some things start fast, then slow down. One example? The acceleration of your car. At first, you gain speed quickly. Eventually, as your car gets closer to its top speed, it accelerates more slowly.

Checkpoint: Point the Way �

Checkpoint: Point the Way �

Checkpoint: Point the Way �

Checkpoint: Point the Way �

Checkpoint: Point the Way �

Checkpoint: Point the Way �

Checkpoint: Point the Way �

Stretching and Shrinking �

Notes: Stretching and Shrinking �

The rules Shrink / stretch factor horizontal shift vertical shift

Checkpoint: Will the following function… � Up Up Up Down Up

Expert Mode: Jigsaw �You’re each going to become an expert in one type of transformation: Left and right Up and down Stretching and shrinking �Take 3 minutes to master your transformation, answering as many questions as you can Fold your answers under the paper

Expert #1: Horizontal Shifts Shrink / stretch factor horizontal shift vertical shift � When we add a number inside the square root, we shift left � When we subtract a number inside the square root, we shift right

Horizontal Shifts: Answer key � Shift left 8 � Shift right 11 Shift left 4 No shift Shift right 5 Shift right 4 Shift left 1 Shift left 9 Shift right 2 Shift left 2 Shift right 3 Shift right 8 Shift left 10 Shift left 3 Shift left 7 Shift right 10

Expert #2: Vertical Shifts Shrink / stretch factor horizontal shift vertical shift � When we add a number outside the square root, we shift up � When we subtract a number outside the square root, we shift down

Vertical Shifts: Answer key � Shift up 8 � Shift up 5 Shift up 4 No shift Shift down 3 Shift down 2 Shift down 6 Shift down 1 Shift down 7 Shift down 8 Shift up 2 Shift up 12 Shift up 9 Shift up 1 Shift down 4 Shift down 14

Expert #3: Vertical Stretch / Shrink / stretch factor horizontal shift vertical shift

Stretch / Shrink: Answer key � Vertical stretch Vertical shrink Vertical stretch No change Vertical shrink Vertical stretch Not a square root function Vertical shrink Vertical stretch

Expert Mode: Jigsaw �Now return to your seats to join with the other experts to solve the problems ahead

Solve as many as you can � Vertical stretch, shift right two, shift up three Vertical stretch, shift left six, shift up one Vertical shrink, shift left four, shift down eight Vertical stretch, shift right seven, no vertical shift Vertical shrink, no horizontal shift, shift up nine No stretch/shrink, shift right three, shift down three Vertical shrink, shift left one, shift up four

Graphing square root functions � No matter what transformations we make, we graph them the same way Make your table (starting with h) Plot the points Connect the dots Work

Graphing square root functions � No matter what transformations we make, we graph them the same way Make your table (starting with h) Plot the points Connect the dots Work

Writing Square Root Functions

Writing Square Root Functions

Writing Square Root Functions Heating Up On Fire

Flooring It Speed (mph) � 2 nd Gear 1 st Gear Time (seconds)

Essential Question �What other relationships can we model?

DOL � 2. Write the function for the square root function below.