Name: ______________________________________ Date: _____________ Period: ______
and its Transformations 𝒚 = 𝒂(𝒙 − 𝒉) 𝟐 + 𝒌
Go to the website: www.geogebra.org
(Follow the geogebra instructions page handout)
1. Type in the following equations and color code and graph all three equations on the graph. 𝑓(𝑥) = 𝑥 2 𝑔(𝑥) =
1
2 𝑥
2 ℎ(𝑥) = −3𝑥 2
Describe the effect that ‘a’ has on the graph:
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2. Type in the following equations and color code and graph all three equations on the graph. 𝑓(𝑥) = 𝑥
2 𝑔(𝑥) = 𝑥
2
+ 5 ℎ(𝑥) = 𝑥 2 − 4
Describe the effect that ‘k’ has on the graph:
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3. Type in the following equations and color code and graph all three equations on the graph. 𝑓(𝑥) = 𝑥
2 𝑔(𝑥) = (𝑥 − 1) 2 ℎ(𝑥) = (𝑥 + 3)
2
Describe the effect that ‘h’ has on the graph:
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4. Now we can put all 3 together to graph:
Graph: 𝑦 = 2(𝑥 + 3)
2
+ 1
5. What would the equation be of 𝑓(𝑥) =
1
2 𝑥
2
when the vertex is transformed to the location (2,-5)?
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For the Quadratic Equations in
use the website below and answer the following questions: https://www.geogebra.org/student/m311077
-Use the website and the toggle bars to see how 𝑎, 𝑏 , and 𝑐 change the graph, answer the following questions:
𝟐
1. Which variable represents the leading coefficient?
2. How does the leading coefficient seem to affect the graph?
3. When changing the leading coefficient is it possible to create a linear function? Explain what causes this.
4. Which variable represents the constant?
5. How does it affect the graph?
6. What does ‘b’ seem to do to your graph?