Quadratic Transformations

Front

What is the effect of adding a constant to the function y = x^2?

Back

The graph is shifted vertically. For example, y = x^2 + 8 shifts the graph up 8 units.

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 of the parabola.

Front

How does the graph of y = x^2 change when it is reflected across the x-axis?

Back

The graph opens downward instead of upward.

Front

What does it mean to compress a quadratic function vertically?

Back

It means to multiply the function by a factor between 0 and 1, making the graph wider.

Front

What transformation occurs when the function f(x) = x^2 is replaced with 2⋅f(x)?

Back

This results in a vertical stretch by a factor of 2.

Front

How do you determine the direction a parabola opens based on the coefficient 'a' in the function y = ax^2?

Back

If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

What is the effect of shifting the graph of y = x^2 to the right by 4 units?

Back

The new function is y = (x-4)^2, moving the vertex to (4, 0).

Front

What happens to the graph of y = x^2 when it is vertically stretched by a factor of 3?

Back

The new function is y = 3x^2, making the graph narrower.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How does the graph of y = -1/2(x-4)^2 + 1 differ from y = x^2?

Back

It is reflected across the x-axis, compressed vertically, and shifted right 4 units and up 1 unit.