Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value indicates the vertical stretch or compression and the direction of the parabola (upward if a > 0, downward if a < 0).

Front

How does the 'h' value in the vertex form affect the graph?

Back

The 'h' value shifts the graph left or right. If h is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

What effect does the 'k' value have in the vertex form?

Back

The 'k' value shifts the graph up or down. If k is positive, the graph shifts up; if negative, it shifts down.

Front

What transformation does the equation y = x² + 8 represent?

Back

The equation y = x² + 8 represents a vertical shift of the graph of y = x² up by 8 units.

Front

What does it mean for a quadratic function to be vertically stretched?

Back

A vertically stretched quadratic function has a greater 'a' value (|a| > 1), making the graph steeper.

Front

What does it mean for a quadratic function to be vertically compressed?

Back

A vertically compressed quadratic function has a smaller 'a' value (0 < |a| < 1), making the graph wider.

Front

How do you identify a reflection in a quadratic function?

Back

A reflection occurs when the 'a' value is negative, causing the parabola to open downward.

Front

What is the effect of shifting a quadratic function to the right?

Back

Shifting a quadratic function to the right involves replacing x with (x - h) in the equation, where h is the number of units to shift.

Front

What is the effect of shifting a quadratic function to the left?

Back

Shifting a quadratic function to the left involves replacing x with (x + h) in the equation, where h is the number of units to shift.