[table][br][tr][br][td]Parabola[/td][br][td]放物線[/td][br][td]포물선[/td][br][td]抛物线[/td][br][/tr][br][tr][br][td]Standard Form[/td][br][td]標準形式[/td][br][td]표준형[/td][br][td]标准形式[/td][br][/tr][br][tr][br][td]Vertex[/td][br][td]頂点[/td][br][td]정점[/td][br][td]顶点[/td][br][/tr][br][tr][br][td]Direction of Parabola[/td][br][td]放物線の方向[/td][br][td]포물선의 방향[/td][br][td]抛物线的方向[/td][br][/tr][br][tr][br][td]Axis of Symmetry[/td][br][td]対称軸[/td][br][td]대칭축[/td][br][td]对称轴[/td][br][/tr][br][tr][br][td]Coefficient[/td][br][td]係数[/td][br][td]계수[/td][br][td]系数[/td][br][/tr][br][tr][br][td]Completing the Square[/td][br][td]平方完成[/td][br][td]완전제곱식으로 변환[/td][br][td]配方法补全平方[/td][br][/tr][br][tr][br][td]Vertex Form[/td][br][td]頂点形式[/td][br][td]정점 형태[/td][br][td]顶点形式[/td][br][/tr][br][tr][br][td]Discriminant[/td][br][td]判別式[/td][br][td]판별식[/td][br][td]判别式[/td][br][/tr][br][tr][br][td]Quadratic Equation[/td][br][td]二次方程式[/td][br][td]이차방정식[/td][br][td]二次方程[/td][br][/tr][br][/table]

[table][br][tr][br][td][b]Factual Questions[/b][/td][br][td][b]Conceptual Questions[/b][/td][br][td][b]Debatable Questions[/b][/td][br][/tr][br][tr][br][td]1. What is the standard form of a parabola?[/td][br][td]1. Why does a parabola open upwards when the coefficient of [math]x^2[/math] is positive?[/td][br][td]1. Is the vertex form more useful than the standard form for graphing parabolas? Why or why not?[/td][br][/tr][br][tr][br][td]2. How do you find the vertex of a parabola given its equation in standard form?[/td][br][td]2. Explain the relationship between the focus, directrix, and vertex of a parabola.[/td][br][td]2. Can parabolas represent real-world situations more effectively than linear functions?[/td][br][/tr][br][tr][br][td]3. What determines the direction (upwards or downwards) of a parabola?[/td][br][td]3. Discuss how the concept of completing the square is used to convert a quadratic equation to vertex form.[/td][br][td]3. Debate the importance of understanding the concept of the focus and directrix in the study of parabolas.[/td][br][/tr][br][tr][br][td]4. How do you find the axis of symmetry for the parabola [math]y=ax^2+bx+c[/math] ?[br][/td][br][td]4. How does changing the value of 'a' in the equation [math]y=ax^2[/math] affect the shape of the parabola?[/td][br][td]4. Discuss the statement: "The properties of parabolas are inherently more complex than those of circles."[/td][br][/tr][br][tr][br][td][br][/td][br][td]5. Compare and contrast the graphs of two parabolas with the same vertex but different orientations.[/td][br][td]5. Evaluate the impact of digital graphing tools on students' understanding of the properties of parabolas.[/td][br][/tr][br][/table][br]

Mini-Investigation: Parabolic Explorations[br][br]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!