Graphing Parabolas
A Grade 10 math worksheet focusing on graphing parabolas, identifying key features, and understanding transformations.
Includes
Standards
Topics
Graphing Parabolas
Name:
Date:
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Read each question carefully and follow the instructions to graph parabolas and identify their key features. Show all your work for full credit.
1. Graph the function y = x² on the coordinate plane below. Identify the vertex and axis of symmetry.
Vertex:
Axis of Symmetry:
For the parabola y = 2(x - 3)² + 1:
2. The vertex of the parabola is at .
3. The axis of symmetry is the line .
4. The parabola opens (upwards/downwards).
5. Which of the following functions represents a parabola that is wider than y = x² and opens downwards?
y = -2x²
y = -0.5x²
y = x² + 3
y = (x + 1)²
6. The graph of y = (x - 4)² has its vertex at (4, 0).
True
False
7. Adding a positive constant 'c' to y = ax² + c shifts the parabola 'c' units to the left.
True
False
8. Graph the function y = -(x + 2)² - 3 on the coordinate plane below. Label the vertex and axis of symmetry.
Vertex:
Axis of Symmetry:
9. Describe the transformations applied to the parent function y = x² to obtain the function y = 3(x - 1)² + 5. Be specific about the direction and magnitude of each transformation.
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