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). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.