Quadratic Transformations

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

What effect does adding a constant to the quadratic function have on its graph?

Back

Adding a constant shifts the graph vertically. For example, y = x² + 8 shifts the graph up 8 units.

Front

What does the transformation y = x² - 4 represent?

Back

The transformation y = x² - 4 represents a downward shift of the graph by 4 units.

Front

How does the transformation y = x² + 2 affect the graph?

Back

The transformation y = x² + 2 moves the graph up by 2 units.

Front

What does the transformation g(x) = (x - 3)² indicate?

Back

The transformation g(x) = (x - 3)² indicates a horizontal shift of the graph to the right by 3 units.

Front

What is the effect of a negative sign in front of a quadratic function, such as f(x) = -x²?

Back

A negative sign reflects the graph over the x-axis.

Front

What does the term 'vertical shift' refer to in quadratic transformations?

Back

Vertical shift refers to moving the graph up or down without changing its shape.

Front

What does the term 'horizontal shift' refer to in quadratic transformations?

Back

Horizontal shift refers to moving the graph left or right without changing its shape.

Front

How do you identify a reflection in a quadratic function?

Back

A reflection occurs when the leading coefficient is negative, such as in f(x) = -x².

Front

What is the effect of changing the coefficient of x² in a quadratic function?

Back

Changing the coefficient affects the width and direction of the parabola. A larger coefficient makes it narrower.