PRECAL.MATH.3.I
Use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k).
Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
characteristicshyperbolaequationcenterhk
Skills
- identify (the characteristics of a hyperbola) #dok1
- write (the equation of a hyperbola given its characteristics and center) #dok2
- analyze (the effect of center (h, k) on the equation of a hyperbola) #dok2
- apply (the characteristics of a hyperbola to derive its equation from a description or graph) #dok3
Learning Targets
- I can identify the characteristics of a hyperbola, such as its center, vertices, foci, and axes. #dok1
- I can write the equation of a hyperbola with center (h, k) given its characteristics. #dok2
- I can analyze how changing the center (h, k) affects the equation of the hyperbola. #dok2
- I can apply knowledge of hyperbolas to derive an equation from a graph or a descriptive scenario. #dok3
Big Ideas
- The equation of a hyperbola can be determined using its characteristics and the location of its center.
- Changing the center of a hyperbola affects its equation and graph, but not its fundamental properties.
Essential Questions
- How do you identify the key characteristics of a hyperbola?
- How does the center (h, k) change the equation of a hyperbola?
- What are the steps to write the equation of a hyperbola given its characteristics and center?
- How are the equations of ellipses and hyperbolas similar and different?
- In what real-world situations could writing the equation of a hyperbola be useful?