Review #5: Quadratic transformations

Front

What is a vertical shift in a quadratic function?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

How does the equation y = x^2 + k transform the graph of y = x^2?

Back

The graph shifts vertically by k units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

What does it mean to vertically stretch a quadratic function?

Back

A vertical stretch occurs when the coefficient of x^2 is greater than 1, making the graph narrower.

Front

What does it mean to vertically compress a quadratic function?

Back

A vertical compression occurs when the coefficient of x^2 is between 0 and 1, making the graph wider.

Front

How does the equation y = -ax^2 transform the graph of y = x^2?

Back

The graph is reflected over the x-axis and vertically stretched if a > 1 or compressed if 0 < a < 1.

Front

What is the vertex of a quadratic function in vertex form y = a(x-h)^2 + k?

Back

The vertex is the point (h, k), which represents the maximum or minimum point of the graph.

Front

What does it mean to reflect a quadratic function over the x-axis?

Back

Reflecting over the x-axis changes the sign of the coefficient of x^2, flipping the graph upside down.

Front

How do you identify the vertex from the standard form of a quadratic function y = ax^2 + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the effect of adding a positive constant to a quadratic function?

Back

Adding a positive constant shifts the graph upward by that constant's value.

Front

What is the effect of subtracting a constant from a quadratic function?

Back

Subtracting a constant shifts the graph downward by that constant's value.