Quadratic Transformations

Front

What is a vertical stretch of a quadratic function?

Back

A vertical stretch occurs when the output values of the function are multiplied by a factor greater than 1, making the graph narrower.

Front

How do you translate a quadratic function down by a certain number of units?

Back

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right involves replacing 'x' with 'x - h' in the function, where 'h' is the number of units to shift.

Front

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

Back

Adding a constant to a quadratic function shifts the graph vertically. If the constant is positive, it shifts up; if negative, it shifts down.

Front

How do you represent a vertical stretch by a factor of 'a'?

Back

Front

What transformation occurs when you replace 'x' with 'x + h' in a quadratic function?

Back

Replacing 'x' with 'x + h' shifts the graph to the left by 'h' units.

Front

What is the standard form of a quadratic function?

Back

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point on the graph, depending on the direction of the parabola.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the coefficient 'a' in the standard form. If 'a' is positive, it opens upwards; if negative, it opens downwards.

Front

What is the effect of a horizontal shift on the graph of a quadratic function?

Back

A horizontal shift moves the graph left or right without changing its shape. It is represented by changing 'x' to 'x - h' or 'x + h'.