Graphing Parabolas
This worksheet focuses on graphing parabolas, identifying key features such as vertex, axis of symmetry, focus, and directrix, and writing equations from given information.
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Graphing Parabolas Worksheet
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Date:
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Carefully read each question and follow the instructions. Show all your work for full credit.
1. For the parabola y = (x - 3)² + 2, identify the following:
a. Vertex:
b. Axis of Symmetry:
c. Direction of Opening:
2. For the parabola x = -2(y + 1)² - 4, identify the following:
a. Vertex:
b. Axis of Symmetry:
c. Direction of Opening:
3. Graph the parabola y = x² - 4x + 3 on the coordinate plane below. Label the vertex and axis of symmetry.
4. Graph the parabola x = -(y - 2)² + 1 on the coordinate plane below. Label the vertex and axis of symmetry.
5. Write the equation of a parabola with vertex (1, -5) and focus (1, -3).
Equation:
6. Write the equation of a parabola with focus (-2, 4) and directrix x = -6.
Equation:
7. Which of the following parabolas opens downwards?
y = 2x² - 3x + 1
y = -x² + 5x - 2
x = (y - 4)² + 3
x = -3(y + 1)² + 6
8. The vertex of the parabola y = -3(x + 2)² - 5 is (-2, -5).
True
False
9. A parabola with a directrix of y = 3 opens upwards.
True
False
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