Question

A parabola opens upward on a coordinate plane. The vertex of the parabola is at the point left-parenthesis 1 comma negative 4 right-parenthesis. The parabola passes through the x axis at x equals negative 1 and x equals 3. It passes through the y axis at y equals negative 3.
Question
Use the graph to answer the question.
The figure shows the graph of the function y equals left-parenthesis x minus 1 right-parenthesis squared minus 4. Identify the x-values for which the function is increasing.
(1 point)
Responses

left-parenthesis x vertical line x greater than negative 4 right-parenthesis
Image with alt text: left-parenthesis x vertical line x greater than negative 4 right-parenthesis

left-parenthesis x vertical line x less than negative 1 or x greater than 3 right-parenthesis
Image with alt text: left-parenthesis x vertical line x less than negative 1 or x greater than 3 right-parenthesis

left-parenthesis x vertical line x greater than 1 right-parenthesis
Image with alt text: left-parenthesis x vertical line x greater than 1 right-parenthesis

left-parenthesis x vertical line x greater-than-or-equal to 0 right-parenthesis

Answer 1

To determine the x-values for which the function \( y = (x - 1)^2 - 4 \) is increasing, we need to analyze the vertex and the general behavior of a parabola.

The vertex of the parabola is at the point \( (1, -4) \). For a parabola that opens upward, the function is decreasing to the left of the vertex and increasing to the right of the vertex. Therefore, the function begins to increase after reaching the vertex.

Since the vertex is at \( x = 1 \), the function is increasing for all \( x \) values greater than \( 1 \).

Thus, the answer is:
**\( (x | x > 1) \)**.