Quadratic Transformations

Front

What is a quadratic transformation?

Back

A quadratic transformation refers to the changes made to the graph of a quadratic function, such as translations, reflections, and stretches/compressions.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x², which is a parabola that opens upwards.

Front

What does a translation of a graph mean?

Back

A translation of a graph means shifting the entire graph horizontally or vertically without changing its shape.

Front

How does the equation g(x) = (x + 4)² transform the graph of f(x) = x²?

Back

It translates the graph 4 units to the left.

Front

What effect does the equation g(x) = (x - 4)² have on the graph of f(x) = x²?

Back

It translates the graph 4 units to the right.

Front

What does reflecting a graph over the x-axis do?

Back

Reflecting a graph over the x-axis flips it vertically, changing the sign of the y-values.

Front

How does the equation g(x) = -x² transform the graph of f(x) = x²?

Back

It reflects the graph over the x-axis.

Front

What does the equation g(x) = x² + 8 do to the graph of f(x) = x²?

Back

It shifts the graph 8 units upward.

Front

What is the effect of a vertical shift on a quadratic graph?

Back

A vertical shift moves the graph up or down without changing its width or direction.

Front

What does a horizontal shift of a graph entail?

Back

A horizontal shift moves the graph left or right, affecting the x-values of the function.