What does 'a' represent in vertex form?
Understand the Problem
The question is asking for clarification on what the variable 'a' means in the vertex form of a quadratic equation. In vertex form, which is typically written as y = a(x - h)² + k, 'a' affects the width and direction (opening up or down) of the parabola.
Answer
'a' represents the vertical stretch or shrink and the direction of the parabola's opening.
The final answer is 'a' represents the vertical stretch or shrink and the direction of the parabola's opening.
Answer for screen readers
The final answer is 'a' represents the vertical stretch or shrink and the direction of the parabola's opening.
More Information
The constant 'a' in the vertex form of a quadratic equation influences both the vertical stretch/shrink of the graph and its orientation. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.
Tips
A common mistake is confusing the role of 'a' with the vertex coordinates (h, k). Remember, 'a' affects the shape and direction, not the position of the vertex.
Sources
- Vertex Form: What Is It? How Do You Calculate It? - PrepScholar Blog - blog.prepscholar.com
- Vertex Form | Equation, Formula & Conversion - Lesson - Study.com - study.com
- Vertex Form - quadratictoolbox.weebly.com
