Parabola Properties Worksheet
Explore the properties of parabolas, including vertex, focus, directrix, and axis of symmetry, with this Grade 9 math worksheet.
Includes
Standards
Topics
Parabola Properties Worksheet
Name:
Date:
Score:
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
Related Worksheets
Rationalizing Radicals Worksheet
Grade 9 Math worksheet focusing on rationalizing single and binomial denominator radicals.
Solving Square Root Equations
Practice solving square root equations with various levels of complexity. This worksheet covers isolating the radical, squaring both sides, and checking for extraneous solutions.
Zero Product Property Worksheet
Practice solving quadratic equations using the Zero Product Property for Grade 9 algebra.
Simplifying Polynomials Worksheet
Grade 9 Math worksheet focusing on simplifying polynomials through addition, subtraction, and multiplication.
Pascal's Triangle Worksheet
Explore the patterns and properties of Pascal's Triangle, including its construction, binomial coefficients, and relationships to other mathematical concepts.
Solving Three-Step Equations
This worksheet provides practice for grade 9 students in solving linear equations that require three steps.
Elimination Method Worksheet
Practice solving systems of linear equations using the elimination method for Grade 9 students.
Rearranging Equations Worksheet
A Grade 9 math worksheet focusing on rearranging algebraic equations to solve for different variables.