Transformations of Quadratics

Front

What is the effect of multiplying a quadratic function by a factor greater than 1, such as in g(x) = 5x² compared to f(x) = x²?

Back

The graph of g(x) is narrower than the graph of f(x).

Front

How does the transformation from y = x² to y = -3x² affect the graph?

Back

The graph is reflected across the x-axis and becomes narrower.

Front

What transformation occurs when the graph of f(x) = x² is shifted to g(x) = (x + 4)²?

Back

The graph is shifted 4 units to the left.

Front

What does the transformation from f(x) = x² to g(x) = -4x² indicate about the graph?

Back

The graph is reflected across the x-axis and is narrower.

Front

If f(x) = x² is the blue graph, what is the red graph if it is described as g(x) = x² - 5?

Back

The red graph is a vertical shift of the blue graph down by 5 units.

Front

What is the general effect of a negative coefficient in front of a quadratic function?

Back

It reflects the graph across the x-axis.

Front

How does a vertical shift affect the graph of a quadratic function?

Back

It moves the graph up or down without changing its shape.

Front

What is the effect of a horizontal shift on the graph of a quadratic function?

Back

It moves the graph left or right without changing its shape.

Front

What does it mean for a quadratic function to be 'narrower'?

Back

It means the graph is steeper and the vertex is closer to the y-axis.

Front

What is the vertex form of a quadratic function?

Back

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