Quadratic Transformations

Front

What does the 'a' value do in the vertex form f(x) = a(x - h)² + k?

Back

The 'a' value determines the vertical stretch or compression of the parabola.

Front

How does changing the 'a' value affect the graph of f(x) = a(x - h)² + k?

Back

Changing 'a' affects the steepness of the graph; if |a| > 1, the graph is vertically stretched (narrower), and if 0 < |a| < 1, it is vertically compressed (wider).

Front

What transformation occurs in the function f(x) = \frac{1}{4}x² compared to the parent function?

Back

This represents a vertical compression (wider) of the parent function.

Front

What does the 'h' value do in the vertex form f(x) = a(x - h)² + k?

Back

The 'h' value shifts the function left or right.

Front

What does the 'k' value do in the vertex form f(x) = a(x - h)² + k?

Back

The 'k' value shifts the function up or down.

Front

What is the effect of a negative 'a' value in the vertex form f(x) = a(x - h)² + k?

Back

A negative 'a' value reflects the graph over the x-axis.

Front

If f(x) = 2(x - 3)² + 1, what transformations are applied to the parent function?

Back

The graph is vertically stretched by a factor of 2, shifted right 3 units, and shifted up 1 unit.

Front

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

Back

A vertically stretched function has a steeper graph compared to the parent function.

Front

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

Back

A vertically compressed function has a less steep graph compared to the parent function.

Front

How do you identify a vertical stretch or compression from the equation f(x) = a(x - h)² + k?

Back

Look at the absolute value of 'a': |a| > 1 indicates a vertical stretch, and 0 < |a| < 1 indicates a vertical compression.