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 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 coefficient starts at values to make f(x) equivalent to g(x).
1 Using the starting values of a, h, and k you see for f(x) in Desmos, rewrite g(x) = x2 in Vertex Form. g(x) =
Magnitude a
2 Try changing the value of a to -4, 0, and 2, graphing each parabola in the squares below. Label the vertex "V" and any roots with "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. Label the vertex "V" and any roots "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. Label the vertex "V" and any roots "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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