Question

Given a quadratic function in vertex form:

Answer 1

Answer:

See below

Step-by-step explanation:

Part A

A vertical stretch takes place when $a\cdot f(x)$ given that  $|a| > 1$

Part B

A vertical compression takes place when $a\cdot f(x)$ given that $0 < |a| < 1$

Part C

A vertical stretch is different than a horizontal compression:

• In a vertical stretch, the input stays the same, but the output is multiplied by the scale factor
• In a horizontal compression, the output stays the same, but the input is multiplied by the scale factor

Part D

A reflection across the x-axis means that the output, our y-variable, is the opposite sign. This means that all values of $a$ must be negative such that $a\cdot f(x)$ as mentioned in parts A and B. Also, in part C, since our scale factor is negative, the output is the only one being multiplied by the scale factor.