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 the function f(x) = \frac{1}{4}x² transform from the parent function?

Back

It undergoes a vertical compression (wider).

Front

Match the equation to its description: Vertically stretched (steeper) by 2 and shifted up 4.

Back

The equation is f(x) = 2(x - 0)² + 4.

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

Back

It reflects the parabola over the x-axis.

Front

What is the vertex of the function f(x) = 3(x - 2)² + 5?

Back

The vertex is (2, 5).

Front

How does the function f(x) = -2(x + 1)² - 3 transform from the parent function?

Back

It is vertically stretched (narrower), reflected over the x-axis, and shifted left 1 and down 3.

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

If f(x) = 4(x - 1)² + 2, what is the effect of the '4' on the graph?

Back

The '4' indicates a vertical stretch (narrower) of the parabola.

Front

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

Back

Changing 'h' shifts the graph left or right.