Question

describe the dilation that occurs when transforming the graph y = x² into the graph y = 3(x + 4)² − 9. stretch horizontally no dilations have been made stretch vertically compress vertically

Explanation:

Step1: Recall Dilation Rules

For a quadratic function in the form \( y = a(x - h)^2 + k \), the coefficient \( a \) determines vertical dilation. If \( |a| > 1 \), it's a vertical stretch; if \( 0 < |a| < 1 \), it's a vertical compression. Horizontal dilation is related to the coefficient inside the parentheses, but here the form is \( (x + 4) \), so the horizontal coefficient is 1 (no horizontal dilation).

Step2: Analyze the Given Functions

The original function is \( y = x^2 \) (where \( a = 1 \)). The transformed function is \( y = 3(x + 4)^2 - 9 \), where \( a = 3 \). Since \( |3| > 1 \), by the vertical dilation rule, this means the graph is stretched vertically.

Answer:

Stretch vertically