The parent function for a quadratic is represented by f(x)=x2

Question

.

Given the function f(x)=(x+10)2−1
. How has it been transformed from the parent function f(x)=x2
?

(1 point)
Responses

Stretch/Compression
Stretch/Compression

Vertical Reflection
Vertical Reflection

Vertical Translation
Vertical Translation

Horizontal Translation

Answer 1

To determine how the function \( f(x) = (x + 10)^2 - 1 \) has been transformed from the parent function \( f(x) = x^2 \), we can analyze the transformations step by step.

1. Horizontal Translation: The \( (x + 10) \) indicates a horizontal translation to the left by 10 units. This is because if you replace \( x \) with \( x + 10 \), you are shifting the graph to the left.

2. Vertical Translation: The \( - 1 \) indicates a vertical translation downward by 1 unit. This shifts the entire graph down.

There are no indications of vertical reflection or stretch/compression in the transformation.

Based on this, the main transformations from the parent function \( f(x) = x^2 \) to \( f(x) = (x + 10)^2 - 1 \) are:

• Horizontal translation left by 10 units
• Vertical translation down by 1 unit

Thus, the correct response related to the transformations would be Horizontal Translation and Vertical Translation. Since the question asks for a single response and does not allow for multiple answers, you might choose one that fits your context, such as Horizontal Translation.