For this page, you’ll need to have Exploring Quadratic Functions(Desmos) open on your computer.
The parabola you’ll see is the graph of 𝑓(𝑥) = 𝑥2 . Another, identical parabola is hiding behind it.
This second parabola is written in Vertex Form: 𝑔(𝑥) = 𝑎(𝑥 - 𝒽)2 + 𝑘. Each coefficient starts at values to make 𝑔(𝑥) equivalent to 𝑓(𝑥).
1 Using the starting values of 𝑎, 𝒽, and 𝑘 you see for 𝑔(𝑥) in Desmos, write the Vertex Form of 𝑓(𝑥) = 𝑥2 : 𝑓(𝑥) =
Magnitude 𝑎
2 Try changing the value of 𝑎 to -4, 0, and 2, graphing each parabola in the squares below. Be sure to identify and label the vertex and any roots with "V" and "R"!
𝑎 = - 4 |
𝑎 = 0 |
𝑎 = 2 |
3 What does 𝑎 tell us about a parabola?
Horizontal Translation 𝒽
4 Set 𝑎 back to 1. Change the value of 𝒽 to -5, 0, and 5, graphing each parabola in the squares below. Be sure to identify and label the vertex and any roots with "V" and "R"!
𝒽 = - 5 |
𝒽 = 0 |
𝒽 = 5 |
5 What does 𝒽 tell us about a parabola?
Vertical Translation 𝑘
6 Set 𝒽 back to 0. Change the value of 𝑘 to -5, 0, and 5, graphing each parabola in the squares below. Be sure to identify and label the vertex and any roots with "V" and "R"!
𝑘 = - 5 |
𝑘 = 0 |
𝑘 = 5 |
7 What does 𝑘 tell us about a parabola?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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