Transformations of Parent Functions Test

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to translate a function up?

Back

Translating a function up means shifting the graph vertically in the positive y-direction by adding a constant to the function.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Front

How does the equation y = (x - 3)² transform the graph of y = x²?

Back

The graph of y = (x - 3)² is translated right 3 units from the parent function y = x².

Front

What effect does the negative sign have in the function y = -x²?

Back

The negative sign reflects the graph of the function over the x-axis.

Front

What does it mean to stretch a function vertically?

Back

Stretching a function vertically means increasing the distance between points on the graph and the x-axis, typically by multiplying the function by a factor greater than 1.

Front

What is the effect of the coefficient in front of x² in y = ax²?

Back

If |a| > 1, the graph is vertically stretched; if 0 < |a| < 1, the graph is vertically compressed.

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is y = |x|.

Front

How does the equation y = 5x² transform the graph of y = x²?

Back

The graph of y = 5x² is vertically stretched by a factor of 5 compared to the parent function y = x².

Front

What does it mean to compress a function vertically?

Back

Compressing a function vertically means decreasing the distance between points on the graph and the x-axis, typically by multiplying the function by a factor between 0 and 1.