5.1 Review Worksheet, Part 1
5.1.1 Using Transformations to Graph Quadratic Functions Graph each function by using a table. 1. f ( x ) = − x 2 + 4 2. g ( x ) = x 2 − 2 x + 1 3. h ( x ) = 2 x 2 + 4 x − 1
Using the graph of f ( x ) = x 2 as a guide, describe the transformations, and then graph each function. 4. g ( x ) = x 2 − 2 5. h ( x ) = ( x + 5) 2 6. j ( x ) = ( x − 1) 2
7. g ( x ) = ( x + 4) 2 − 3
8. h ( x ) = ( x + 2) 2 + 2
9. j ( x ) = ( x − 4) 2 − 9
2
= g x x ( ) 4 7 2
1 3
10.
11. h ( x ) = − 20 x 2
12.
j x
x
( )
=
Use the description to write each quadratic function in vertex form. 13. The parent function f ( x ) = x 2 is reflected across the x -axis, vertically compressed by a factor of 1 2 , and translated 1 unit right to create g .
14. The parent function f ( x ) = x 2 is vertically stretched by a factor of 2.5 and translated 2 units left and 1 unit up to create h .
15. The average gas mileage m in miles per gallon for a compact car is modeled by m ( s ) = − 0.015( s − 47) 2 + 33, where s is the car’s speed in miles per hour. The average gas mileage for an SUV is modeled by m u ( s ) = − 0.015( s − 47) 2 + 15. What kind of transformation describes this change, and what does this transformation mean?
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