GeoGebra Classroom

# Investigating general parabola (AASL 2.6)

## Keywords

 Parabola 放物線 포물선 抛物线 Standard Form 標準形式 표준형 标准形式 Vertex 頂点 정점 顶点 Direction of Parabola 放物線の方向 포물선의 방향 抛物线的方向 Axis of Symmetry 対称軸 대칭축 对称轴 Coefficient 係数 계수 系数 Completing the Square 平方完成 완전제곱식으로 변환 配方法补全平方 Vertex Form 頂点形式 정점 형태 顶点形式 Discriminant 判別式 판별식 判别式 Quadratic Equation 二次方程式 이차방정식 二次方程
 Factual Questions Conceptual Questions Debatable Questions 1. What is the standard form of a parabola? 1. Why does a parabola open upwards when the coefficient of is positive? 1. Is the vertex form more useful than the standard form for graphing parabolas? Why or why not? 2. How do you find the vertex of a parabola given its equation in standard form? 2. Explain the relationship between the focus, directrix, and vertex of a parabola. 2. Can parabolas represent real-world situations more effectively than linear functions? 3. What determines the direction (upwards or downwards) of a parabola? 3. Discuss how the concept of completing the square is used to convert a quadratic equation to vertex form. 3. Debate the importance of understanding the concept of the focus and directrix in the study of parabolas. 4. How do you find the axis of symmetry for the parabola ? 4. How does changing the value of 'a' in the equation affect the shape of the parabola? 4. Discuss the statement: "The properties of parabolas are inherently more complex than those of circles." 5. Compare and contrast the graphs of two parabolas with the same vertex but different orientations. 5. Evaluate the impact of digital graphing tools on students' understanding of the properties of parabolas.
Mini-Investigation: Parabolic Explorations Welcome to Parabolic Explorations! Today, we're diving into the curvy world of parabolas with a fun mini-investigation. Grab your graphing tools, a sprinkle of curiosity, and let's get started!

1. Parabolic Patterns: Notice the equation What happens if you change the value of 'a' value? How does the parabola change?

2. The Discriminant Discovery: The discriminant in our quadratic formula is . Play around with different '', '', and '' values. Can you find a set of values where the discriminant is zero? What does this tell you about the graph?

## The b^2-4ac is called the discriminant. In the applet above you may have discovered what it tell us about the number of solutions.

3. Axis of Symmetry: The vertical pink line is called the axis of symmetry. If we change '', ' and '' which parameters affects the axes of symmetry? How can the axes of symmetry be calculated?

## Extension

4. Vertex Venture: As you change the '' value. How does the vertex move? Can you work out the path of the vertex in terms of ?

## Extension

5.Vertex Venture: As you change the '' value. How does the vertex move? Can you work out the path of the vertex in terms of ?