Transforming Parabolas Worksheet
Grade 10 math worksheet focusing on transformations of parabolas, including translations, reflections, and dilations from the parent function y = x².
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Transforming Parabolas
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Read each question carefully and follow the instructions to transform the given parabolas or identify the transformations.
1. Which of the following transformations would change the graph of y = x² to y = (x - 3)² + 2?
Shift right 3 units, shift up 2 units
Shift left 3 units, shift up 2 units
Shift right 3 units, shift down 2 units
Shift left 3 units, shift down 2 units
2. The parabola y = -2x² is a reflection of y = x² across the x-axis and a vertical stretch by a factor of:
1/2
2
-2
-1/2
3. The vertex of the parabola y = (x + 5)² - 1 is at ( , ).
4. A vertical compression of the parabola y = x² by a factor of 1/3 results in the equation y = x².
5. Graph the parent function y = x² and the transformed function y = -(x + 1)² + 3 on the same coordinate plane. Clearly label both parabolas.
6. The graph of y = x² + 4 is a vertical shift of the parent function y = x² up by 4 units.
True
False
7. A horizontal stretch of y = x² would result in an equation of the form y = (bx)² where |b| > 1.
True
False
8. Describe the sequence of transformations that map the graph of y = x² to the graph of y = -1/2(x - 4)² - 7.