For this page, you’ll need to have Exploring Quadratic Functions (Desmos) open to Slide 1: Transforming Parabolas.
The parabola you’ll see is the graph of g(x) = x2 . Another, identical parabola is hiding behind it.
This second parabola is written in Vertex Form: f(x) = a(x - h)2 + k. Each model setting starts at the value that makes f(x) equivalent to g(x).
1 Use the starting values of a, h, and k you see in Desmos, to complete this equation: g(x) = x2 = f(x) = (x - )2 +
Magnitude a
2 In the first square below, make a sketch of the original graph you see (a = 1, h = 0, k = 0).
Then try changing the value of a to 10, 0.1, 0, -10 and -2, graphing each parabola in the squares below. Label the vertex "V" and any roots with "R"!
a = 1 |
a = 10 |
a = 0.1 |
a = 0 |
a = - 10 |
a = - 2 |
3 What does a tell us about a parabola?
Translation
| Horizontal Translation h | Vertical Translation k |
|---|---|
Set a back to 1. Change the value of h to -5 and 5, graphing each parabola in the squares below. |
Set h back to 0. Change the value of k to -5 and 5, graphing each parabola in the squares below. |
h = - 5 |
h = 5 |
k = - 5 |
k = 5 |
Label the vertex "V" and any roots "R"! |
Label the vertex "V" and any roots "R"! |
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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