Factorising quadratics, sketching and inequalities

Keywords

English	Japanese	Korean	Chinese Simplified
Factorise/Factorize	因数分解	인수분해	因式分解
Quadratic Equation	二次方程式	이차방정식	二次方程
Roots	根	근	根
X-axis Intersection	X軸との交点	x축과의 교점	与x轴的交点
Graph Sketching	グラフのスケッチ	그래프 스케치	绘图
Discriminant	判別式	판별식	判别式
Leading Coefficient	最高次係数	선도계수	首项系数
Orientation of Quadratic Graph	二次関数のグラフの向き	이차함수 그래프의 방향	二次图形的方向
Completing the Square	平方完成	완전제곱식	配方法
Quadratic Formula	二次方程式の解の公式	이차방정식의 해 공식	二次方程的求根公式
Solution Regions	解の領域	해의 영역	解的区域
Quadratic Inequalities	二次不等式	이차부등식	二次不等式
Factored Form	因数分解された形	인수분해된 형태	因式分解形式
Perfect Square	完全平方	완전제곱	完全平方
Critical Values	臨界値	임계값	临界值

Factual Questions	Conceptual Questions	Debatable Questions
1. How do you factorise a quadratic equation in the form ?	1. Explain the significance of the discriminant in solving quadratic equations.	1. Is factoring always the most efficient method for solving quadratic equations? Why or why not?
2. What are the roots of the quadratic equation ?	2. Discuss how the sign of the leading coefficient affects the orientation of a quadratic graph.	2. Debate the importance of learning to sketch quadratic graphs by hand in the age of graphing calculators.
3. How do you determine if a quadratic graph will touch or intersect the x-axis?	3. How does factoring a quadratic equation help in sketching its graph?	3. Can understanding inequalities and their graphical representations enhance problem-solving skills in real-life situations?
4. Sketch the graph of	4. Compare and contrast the methods of solving quadratic equations: factoring, completing the square, and using the quadratic formula.	4. Discuss the statement: "The ability to solve quadratic equations is more crucial than understanding their graphical implications."
5. What is the solution to the inequality?	5. Explain the concept of "solution regions" in quadratic inequalities.	5. Evaluate the role of quadratic equations and their applications in higher mathematics and other disciplines.

Mini-Investigation: The Quest for Quadratic Mastery

Mini-Investigation: The Quest for Quadratic Mastery Welcome, math adventurer, to the Quest for Quadratic Mastery! Today's challenge is to unlock the secrets of factoring quadratics. Prepare your algebraic skills, and let's crack these puzzles! Complete these quests, and you shall be crowned the Quadratic Master! Remember, each equation is a puzzle waiting to be solved. Enjoy the journey!

Explain a method for factorising quadratics with a worked example. (The videos explain a process, do you have a different method?)

Factorising quadratics

Factorising harder quadratics

1. Simple Squares: Look at the quadratic equation = 0. It seems to be a perfect square! How can you identify perfect squares? What does the graph of a perfect square parabola look like?

2. Significance of Signs: How does the sign of the solutions relate to the original equation?

3. Reverse Engineering: Imagine you're a mathematician who loves the number 3. Create a quadratic equation that has 3 and -3 as its solutions. What does your equation look like?

4. Creative Coefficients: Design your own factorable quadratic equation. Challenge a friend to factor it. Can they do it without using the quadratic formula?

5. Quadratic Challenge: Find a quadratic equation that is impossible to factor with whole numbers. What does the graph of such an equation look like?