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Effects of a, h, and k to the Graph of Quadratic Functions
Did you enjoy the activity? To better understand the transformation of the graph of a quadratic function, read some key concepts.
Key Concepts on the Graph of Quadratic Functions
Key Concepts on the Graph of Quadratic Functions
In the graph of y = ax^2 + bx + c, the larger the a is, the narrower is the graph.
In the graph of y = ax^2 + bx + c, the larger the a is, the narrower is the graph.
If a >0, the parabola opens downward. If a<0, the parabola opens downward.
If a >0, the parabola opens downward. If a<0, the parabola opens downward.
To graph y = a ( x – h )^2 , slide the graph of y = ax^2 horizontally h units. If h > 0, slide it to the right, if h < 0, slide it to the left. The graph has vertex (h,0) and its axis is the line x=h.
To graph y = a ( x – h )^2 , slide the graph of y = ax^2 horizontally h units. If h > 0, slide it to the right, if h < 0, slide it to the left. The graph has vertex (h,0) and its axis is the line x=h.
To graph y = a x^2 +k, slide the graph of y = ax^2 vertically k units. If k > 0, slide it upward, if k < 0, slide it downward. The graph has vertex (0,k) and its axis is the line x=0 (y-axis).
To graph y = a x^2 +k, slide the graph of y = ax^2 vertically k units. If k > 0, slide it upward, if k < 0, slide it downward. The graph has vertex (0,k) and its axis is the line x=0 (y-axis).
To graph y = a (x-h)^2 +k, slide the graph of y = ax^2 horizontally h units and vertically k units. The graph has vertex (h,k) and its axis of symmetry is the line x=h.
To graph y = a (x-h)^2 +k, slide the graph of y = ax^2 horizontally h units and vertically k units. The graph has vertex (h,k) and its axis of symmetry is the line x=h.
Vertex of the graph of a quadratic function:
Vertex of the graph of a quadratic function:
In standard form f(x) = a(x-h)^2 +k, the vertex (h,k) can be directly obtained from the values of h and k.
In general form f(x) = ax^2 +bx + c, the vertex (h,k) can be obtained using the formula,
Your goal in this section is to apply mathematical concepts that you have learned in graphing quadratic functions. Use these mathematical concepts to perform the provided activities in this section.
Your goal in this section is to apply mathematical concepts that you have learned in graphing quadratic functions. Use these mathematical concepts to perform the provided activities in this section.
Activity 3:
Activity 3:
Be My Graph!
Be My Graph!
Activity 4:
Activity 4:
Translate Me!
Translate Me!
Webquest Activity:
Webquest Activity:
Math is all Around!
Math is all Around!
Make a simple presentation of world famous parabolic arches.
Make a simple presentation of world famous parabolic arches.
TASK
TASK
Begin the activity by forming a group of 5 members. Choose someone you can depend on to work diligently and to do this fair share of work.
2. In your free time, start surfing the net for world famous parabolic arches. As you search, keep a record of where you go, and what you find on the site.
3. Complete the project by organizing the data you collected, including the name of the architect and the purpose of creating the design.
4. Once you have completed the data, present it to the class in a creative manner. You can use any of the following but not limited to them.
Multimedia presentation
Webpages
Posters
5. You will be assessed based on the rubric for this activity.
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