Transformation of Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

Front

How does the equation y = x² + 5 represent a transformation?

Back

This equation represents a vertical translation of the parent function y = x², shifted up 5 units.

Front

What transformation does y = (x + 4)² represent?

Back

This equation represents a horizontal translation of the parent function y = x², shifted left 4 units.

Front

What is the effect of the term (x - h) in a quadratic function?

Back

The term (x - h) indicates a horizontal shift to the right by h units if h is positive, and to the left if h is negative.

Front

What does the coefficient 'a' in a quadratic function affect?

Back

The coefficient 'a' affects the width and direction of the parabola; if a > 1, the parabola is narrower, and if a < 1, it is wider. If a < 0, the parabola opens downwards.

Front

Describe the transformation of f(x) = (x - 3)² + 5.

Back

This function represents a rightward shift of 3 units and an upward shift of 5 units from the parent function y = x².

Front

What does the absolute value in f(x) = 3|x + 8| indicate?

Back

The absolute value indicates that the function will reflect any negative values of (x + 8) above the x-axis, creating a V-shaped graph.

Front

How does the transformation f(x) = 3|x + 8| affect the parent function?

Back

This function stretches the parent function vertically by a factor of 3 and shifts it left by 8 units.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x², which is the simplest form of a quadratic function.