IM2 Transforming Quadratic Functions

Front

What happens to the vertex of the graph when the function changes from f(x) = 3x² - 1 to f(x) = 3(x - 2)² - 1?

Back

The vertex of the graph will move right 2 units.

Front

Which quadratic function is the widest?

Back

y = -¼x².

Front

How does the graph of y = 2x² + 3 differ from y = 2x²?

Back

It is shifted 3 units up.

Front

Which function represents a translation of 3 units to the left?

Back

f(x) = (x + 3)² + 1.

Front

Which function has a translation of 2 units right and a vertical stretch by a factor of 5?

Back

f(x) = 5(x - 2)².

Front

What is the effect of changing the coefficient of x² in a quadratic function?

Back

It affects the width and direction of the parabola.

Front

What does it mean for a quadratic function to have a vertical stretch?

Back

The graph becomes narrower as the coefficient of x² increases.

Front

How does the graph of f(x) = x² compare to f(x) = -x²?

Back

f(x) = -x² opens downwards, while f(x) = x² opens upwards.

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

It indicates the horizontal shift of the graph.