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Discovering Quadratic Transformations

Last updated almost 4 years ago
10 questions
y = x2 is called the "parent function" of all quadratic functions. It is the most basic form of a quadratic function and can be transformed in infinitely many ways to create all other quadratic functions. We call it the "parent function" because we use it as a starting point from which to create other quadratic functions. Use the problems below to create graphs and visualize what transformations are being made to the parent function.
1

Graph x2 and x2 + 4 in desmos

1

What transformation occurred when x2 became x2 + 4?

1

Graph x2 and x2 - 6 in desmos

1

What transformation occurred when x2 became x2 - 6?

1

Graph x2 and (x - 1)2 in desmos

1

What transformation occurred when x2 became (x - 1)2?

1

Graph x2 and (x + 2)2 in desmos

1

What transformation occurred when x2 became (x + 2)2?

1

Match the function to its transformation from the parent function

Draggable itemCorresponding Item
(x + 4)2
moved up 4 places
(x - 5)2
moved down 4 places
x2 + 4
moved right 4 places
(x - 4)2
moved left 4 places
x2 - 4
moved up 5 places
x2 - 5
moved down 5 places
(x + 5)2
moved left 5 places
x2 + 5
moved right 5 places
1

What would happen to the parent function if it became y = (x - 3)2 + 5?