Question

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

A U-shaped function is graphed on the coordinate plane.
▼Click for Long Desc
From left to right, the x-axis has numbers from negative 10 to 10 in increments of 1. From bottom to top, the y-axis has numbers from negative 10 to 10 in increments of 1. From left to right, the function decreases as it passes through the points left parenthesis 4 comma 3 right parenthesis, left parenthesis 5 comma negative 2 right parenthesis, and left parenthesis 6 comma negative 5 right parenthesis until it reaches a minimum at left parenthesis 7 comma negative 6 right parenthesis. The function then increases as it passes through the points left parenthesis 8 comma negative 5 right parenthesis, left parenthesis 9 comma negative 2 right parenthesis, and left parenthesis 10 comma 3 right parenthesis.

A U-shaped function is graphed on the coordinate plane.
▼Click for Long Desc
From left to right, the x-axis has numbers from negative 10 to 10 in increments of 1. From bottom to top, the y-axis has numbers from negative 10 to 10 in increments of 1. From left to right, the function decreases as it passes through the points left parenthesis 2 comma 9 right parenthesis, left parenthesis 3 comma 2 right parenthesis, left parenthesis 4 comma negative 3 right parenthesis, and left parenthesis 5 comma negative 6 right parenthesis until it reaches a minimum at left parenthesis 6 comma negative 7 right parenthesis. The function then increases as it passes through the points left parenthesis 7 comma negative 6 right parenthesis, left parenthesis 8 comma

Answer 1

Choose the second graph (the one with a minimum at (6, −7)).

Reason: y = (x−6)^2 − 7 is a parabola in vertex form with vertex (6, −7), opens upward, and passes through (5, −6), (4, −3), (3, 2), (2, 9), (7, −6), etc., which matches the second description.