Question

Identify how the parent function y=x² was transformed to create the given function y=-25x² + 6.

a) Vertical compression by a factor of 25, shift 6 units downward
b) Vertical compression by a factor of 6, shift 25 units downward
c) Vertical stretch by a factor of 25, shift 6 units upward
d) Vertical stretch by a factor of 6, shift 25 units upward

Answer 1

The function y=-25x² + 6 represents a vertical stretch of the parent function y=x² by a factor of 25, with a shift of 6 units upward. The correct answer is c) Vertical stretch by a factor of 25, shift 6 units upward.

Step-by-step explanation:

The transformation of the parent function y=x² to create the given function y=-25x² + 6 leads us to recognize several changes:

• The presence of the negative sign before the 25 indicates a reflection across the x-axis.
• The coefficient 25 suggests a vertical stretching or compression by a factor of 25.
• The addition of 6 at the end denotes a vertical shift.

Since a larger coefficient than 1 stretches the graph, and a smaller one compresses it, the correct transformation is a:

c) Vertical stretch by a factor of 25, shift 6 units upward.

Therefore, the original function has been vertically stretched, not compressed, because the value 25 is greater than 1, and the positive sign on 6 indicates an upward shift, not downward.