Transforming Parabolas Worksheet
Grade 12 math worksheet on transforming parabolas, including translations, reflections, stretches, and compressions.
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Transforming Parabolas
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Read each question carefully and follow the instructions. Show all your work for full credit.
1. Which transformation describes the change from y = x² to y = (x - 3)² + 2?
Shift left 3, up 2
Shift right 3, up 2
Shift left 3, down 2
Shift right 3, down 2
2. The parabola y = -2x² is a of y = x².
Vertical stretch by factor of 2, reflected across x-axis
Vertical compression by factor of 2, reflected across x-axis
Horizontal stretch by factor of 2, reflected across y-axis
Horizontal compression by factor of 2, reflected across y-axis
3. The vertex form of a parabola is y = a(x - h)² + k, where (h, k) represents the .
4. A negative value for 'a' in y = a(x - h)² + k indicates a across the x-axis.
5. Describe the transformations applied to the parent function y = x² to obtain the function y = 0.5(x + 4)² - 1. Include a graph of the transformed parabola.
Match each transformation with its effect on the parabola y = x².
6. y = (x + 5)²
a. Vertical stretch
7. y = x² - 7
b. Shift left
8. y = 3x²
c. Shift down
9. y = -x²
d. Reflection across x-axis
10. Write the equation of a parabola that has been vertically compressed by a factor of 1/3, reflected across the x-axis, and shifted right 2 units and up 5 units from the parent function y = x².