Quadratic Transformations

Front

What happens to the graph of f(x) = ax² when 0 < a < 1?

Back

The graph becomes wider or vertically compressed.

Front

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

Back

Vertical compression (wider).

Front

What is the vertex of the equation y = (x + 4)² - 6?

Back

(-4, -6).

Front

If f(x) is transformed to g(x), which equation represents g(x) if it shifts right by 3 units?

Back

g(x) = f(x - 3).

Front

Which equation represents the transformation: up 4, stretched 3, reflected down, and left 1?

Back

f(x) = -3(x + 1)² + 4.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does a negative 'a' value in f(x) = ax² indicate about the graph?

Back

The graph opens downward.

Front

How does changing 'a' in f(x) = ax² affect the width of the parabola?

Back

If |a| > 1, the graph becomes narrower; if 0 < |a| < 1, it becomes wider.

Front

What is the effect of adding a constant 'k' to f(x) = ax²?

Back

It shifts the graph vertically by 'k' units.

Front

What does the transformation f(x) = f(x) + 3 do to the graph?

Back

It shifts the graph up by 3 units.