Select the graph of the function y=(x−6)2−7

Question

.(1 point)
Responses

A U-shaped function is graphed on the coordinate plane.
Image with alt text: A U-shaped function is graphed on the coordinate plane.

A U-shaped function is graphed on the coordinate plane.
Image with alt text: A U-shaped function is graphed on the coordinate plane.

A U-shaped function is graphed on the coordinate plane.
Image with alt text: A U-shaped function is graphed on the coordinate plane.

A U-shaped function is graphed on the coordinate plane.
Image with alt text: A U-shaped function is graphed on the coordinate plane.
Remaining Attempts : 3
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a b c or d

Answer 1

To determine the correct graph of the function \( y = (x - 6)^2 - 7 \), we should analyze its properties:

1. Shape: The function is a quadratic, represented in vertex form \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. For this function, the vertex is at \( (6, -7) \).

2. Direction: Since the coefficient of the squared term (which is 1 here) is positive, the parabola opens upwards (U-shaped).

3. Vertex: The vertex of the graph is at the point (6, -7). This point is the lowest point on the graph (since it opens upwards).

Given this information, look for a U-shaped graph that has a vertex at (6, -7). This will help you determine which graph accurately represents the function \( y = (x - 6)^2 - 7 \).

If you provide the graphs labeled a, b, c, or d, I can help identify which one corresponds to this analysis.