Characteristics of Parabolas Worksheet
Explore and identify the key characteristics of parabolas, including vertex, focus, directrix, and axis of symmetry.
Includes
Standards
Topics
Characteristics of Parabolas
Name:
Date:
Score:
Read each question carefully and provide the most accurate answer. Show all your work for full credit.
1. For the parabola with equation (x - 3)² = 8(y + 1), identify the following characteristics:
a) Vertex:
b) Focus:
c) Directrix:
d) Axis of Symmetry:
2. Which of the following equations represents a parabola that opens downwards?
y = 2x² + 3x - 1
x = -y² + 5y + 2
y = -x² - 4x + 7
x = 3y² - y + 1
3. The is a fixed point not on the parabola, and the is a fixed line not intersecting the parabola.
4. The distance from any point on a parabola to the focus is equal to its distance to the .
5. Consider the parabola given by the equation y² + 4y + 8x - 4 = 0.
a) Rewrite the equation in standard form.
b) Find the vertex, focus, and directrix.
c) Sketch the graph of the parabola on the coordinate plane below, labeling the vertex, focus, and directrix.
6. All parabolas have a vertical axis of symmetry.
True
False
7. The latus rectum of a parabola is a line segment through the focus, perpendicular to the axis of symmetry, with endpoints on the parabola.
True
False
8. Derive the equation of a parabola with its vertex at the origin (0,0) and its focus at (0, p).
Related Worksheets
Perfect Square Trinomials
This worksheet focuses on identifying, factoring, and constructing perfect square trinomials, essential skills for Grade 12 Algebra.
Solving Square Root Equations
This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 12 Algebra students.
Finding Polynomial Functions from Graphs
Grade 12 math worksheet on determining polynomial functions given their graphs, focusing on roots, multiplicity, and end behavior.
Combining Polynomials Worksheet
Grade 12 math worksheet on combining polynomials, including addition, subtraction, multiplication, and division.
Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
Grade 12: Rearranging Equations
This worksheet focuses on rearranging complex algebraic equations to solve for specific variables, suitable for Grade 12 mathematics.
Grade 12: Rearranging Equations
This worksheet focuses on rearranging complex algebraic equations to solve for specific variables, suitable for Grade 12 mathematics.
Direct Variation Worksheet
A Grade 12 mathematics worksheet focusing on direct variation, including identifying direct variation, writing equations, and solving problems.