Parabola Properties Worksheet
Explore the properties of parabolas, including vertex, focus, directrix, and axis of symmetry, with this Grade 9 math worksheet.
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Parabola Properties Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. A parabola is the set of all points in a plane that are equidistant from a fixed point, called the , and a fixed line, called the .
2. The point on the parabola that is closest to the directrix is called the .
3. The line passing through the focus and the vertex of a parabola is called the of symmetry.
1. Which of the following equations represents a parabola opening upwards?
y = -2x² + 3x - 1
x = y² - 4y + 2
y = x² + 5x + 6
x = -3y² + y - 5
2. The standard form of a parabola with a vertical axis of symmetry is:
(x - h)² = 4p(y - k)
(y - k)² = 4p(x - h)
Ax + By + C = 0
x²/a² + y²/b² = 1
1. For the parabola with equation (x - 3)² = 8(y + 1):
a. Identify the vertex.
b. Identify the focus.
c. Write the equation of the directrix.
d. Write the equation of the axis of symmetry.
2. Sketch the parabola given by the equation x² = -4y on the coordinate plane below. Label the vertex, focus, and directrix.
1. The latus rectum of a parabola passes through the vertex.
True
False
2. All parabolas have a horizontal or vertical axis of symmetry.
True
False
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