SUMMARY
The standard form of the equation for a parabola with an axis of symmetry along the x-axis (y=0) and a focus at (-5,0) is derived from the definition of a parabola. The correct equation format is x = a(y - k)² + h, where (h, k) is the vertex. Given the focus, the vertex is located at (-5,0), and the equation can be expressed as x = a(y - 0)² - 5. The value of 'a' can be determined based on the distance from the vertex to the focus.
PREREQUISITES
- Understanding of conic sections, specifically parabolas
- Familiarity with the vertex form of a parabola equation
- Knowledge of the focus and directrix properties of parabolas
- Ability to manipulate quadratic equations
NEXT STEPS
- Study the vertex form of a parabola equation in detail
- Learn how to derive the equation of a parabola from its focus and directrix
- Practice problems involving the conversion of standard form equations of parabolas
- Explore examples of parabolas with different orientations and their equations
USEFUL FOR
Students learning conic sections, particularly those studying parabolas, as well as educators seeking to provide clear examples of deriving equations from geometric properties.