EXPLORING QUADRATIC FUNCTION

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Learning Objectives:
[list=1][*][b]Identify the Definition of Quadratic Function[/b]: Students are expected to understand the definition and basic concepts of quadratic functions through interactive exploration in GeoGebra.[/*][*][b]Explaining the Relationship of Coefficients to Graphs[/b]: Students will learn how the coefficients in the quadratic equation (a, b, ) and (c) affect the shape and position of the graph of a quadratic function.[br]Using Tables to Determine Function Values: Through GeoGebra, students can learn how to determine the value of a quadratic function by using a table of values.[/*][*][b]Drawing Graphs of Quadratic Functions[/b]: Students will be trained to draw the graph of a quadratic function accurately using GeoGebra features.[/*][*][b]Understanding Properties of Graphs of Quadratic Functions[/b]: Students will investigate how changes in coefficient values affect the properties of the graph, such as curvature, axis of symmetry, and vertex.[/*][*][b]Applying Concepts in Problem Solving[/b]: Students will use GeoGebra to apply quadratic function concepts in solving math problems related to real or theoretical situations.[br][/*][*][b]Developing Critical Thinking Skills[/b]: With GeoGebra, students are expected to think critically in distinguishing between quadratic and non-squared functions and understanding their characteristics.[/*][*][b]Collaboration and Discussion[/b]: Students will work together in groups to discuss and present their findings related to quadratic functions, strengthening their collaborative and communication skills.[/*][*][b]Using Innovative Learning Media[/b]: GeoGebra as an interactive learning media will help students to be more engaged and motivated in learning math.[/*][/list]By using GeoGebra, students not only learn math concepts but also develop digital and analytical skills essential for 21st century learning.
Activity Instructions:
1. Understand the qudratic function material provided[br]2. Watch the applet and answer the questions provided[br]3. Direct observation with illustrations using your Ideas[br]4. Practice by answering the questions provided[br]5. Give criticism and suggestions related to today's learning[br]6. Understand the references as a form of learning
What are quadratic function?
A quadratic function is represented by the standard form, [math]y=ax^2+bx+c[/math][br]
Condition and Term:
In order for such an equation to be a quadratic function, and not a linear one, we must have that the coefficient a is not equal to zero; i.e. a ≠ 0
The graph of a quadratic function is a parabola
The larger the absolute value of a is, the thinner the shape of the parabola becomes. The smaller the absolute value, the wider the parabola becomes
The coefficient a is also an indicator of the direction of the shape of the parabola
If the value of a is positive, the parabola opens upwards. If the value of a is negative, the parabola opens downwards
Additional
Graph linear and quadratic functions and show intercepts, maxima and minima
Quadratic Function Characteristics:
How to formulate?
Video of the material:
Example:
a=-1, b=10, c=9[br][math]y=-1x^2+10x+9[/math]
Draw the shape of the graph! Analyze how the graph changes as you move the sliders!
Find the x-intercepts of the quadratic function!
Discover where the y-intercept, vertex and axis of symmetry lie on the graph!
After looking at the example problem above along with the applet, now it's time for you to try doing it yourself.
a=7, b=5, c=3[br][math]y=7x^2+5x+3[/math]
Draw the shape of the graph! Analyze how the graph changes as you move the sliders!
Find the x-intercepts of the quadratic function!
Discover where the y-intercept, vertex and axis of symmetry lie on the graph!
Multiple Choices
Which of the following are the x-intercepts of the quadratic function from second applet graph?
Essay:
Where the y-intercept, vertex and axis of symmetry lie on the third applet graph?
Reference
Reflection:
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