Transformation of Quadratic Functions

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 with its vertex at the origin (0,0).

Front

What does a vertical shift of a quadratic function mean?

Back

A vertical shift means moving the graph up or down. For example, f(x) = x² + 3 shifts the graph up 3 units.

Front

What does a horizontal shift of a quadratic function mean?

Back

A horizontal shift means moving the graph left or right. For example, f(x) = (x - 2)² shifts the graph right 2 units.

Front

How do you represent a vertical shift down in a quadratic function?

Back

To represent a vertical shift down, subtract a value from the function. For example, f(x) = x² - 4 shifts the graph down 4 units.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

A negative sign reflects the graph across the x-axis. For example, f(x) = -x² opens downwards instead of upwards.

Front

What is the transformation of f(x) = (x + 3)²?

Back

This represents a horizontal shift left 3 units from the parent function f(x) = x².

Front

What does the equation f(x) = (x - 1)² - 5 represent?

Back

This represents a horizontal shift right 1 unit and a vertical shift down 5 units from the parent function.

Front

How do you identify the vertex of a quadratic function in vertex form?

Back

In vertex form, f(x) = a(x - h)² + k, the vertex is at the point (h, k).

Front

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

Back

Adding a constant shifts the graph vertically. For example, f(x) = x² + 2 shifts the graph up 2 units.

Front

What does the term 'compression' mean in relation to quadratic functions?

Back

Compression refers to making the graph narrower. For example, f(x) = 2x² is a vertical compression compared to f(x) = x².