Quadratic Function Transformations

Front

What is the parent function of a quadratic function?

Back

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

Front

What effect does a vertical shift have on the graph of a quadratic function?

Back

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

Front

How does the coefficient of x² affect the width of the parabola?

Back

If the coefficient is greater than 1, the parabola is narrower; if it is between 0 and 1, the parabola is wider.

Front

What transformation is represented by the equation y = x² + 2?

Back

This equation represents a vertical shift of the parent function up by 2 units.

Front

What does a negative coefficient in front of x² indicate about the parabola?

Back

A negative coefficient indicates that the parabola opens downward.

Front

How do you identify a reflection in the x-axis for a quadratic function?

Back

A reflection in the x-axis occurs when the coefficient of x² is negative.

Front

What is the transformation represented by the equation g(x) = -3x²?

Back

This equation represents a reflection in the x-axis and a vertical stretch by a factor of 3.

Front

What does the term 'vertical stretch' mean in the context of quadratic functions?

Back

A vertical stretch means that the graph is pulled away from the x-axis, making it narrower.

Front

How does the transformation y = x² - 5 affect the graph of the parent function?

Back

This transformation represents a vertical shift down by 5 units.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant shifts the graph vertically without changing its shape.