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Advanced Math / Nonlinear functions Difficulty: Easy

The graph shows a marble's height above the ground $y$ , in inches, $x$ seconds after it started moving on an elevated track of a marble run. Which of the following is the best interpretation of the $y$ -intercept of the graph?

The marble's height was $0$ inches above the ground $8$ seconds after it started moving.

The marble's height was $8$ inches above the ground when it started moving.

The marble's minimum height was $0$ inches above the ground.

The marble's minimum height was $8$ inches above the ground.

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Explanation

Choice B is correct. The y-intercept of a graph is the point at which the graph intersects the y-axis. The graph shown intersects the y-axis at the point $left parenthesis 0 comma 8 right parenthesis$ . Therefore, the y-intercept of the graph is $left parenthesis 0 comma 8 right parenthesis$ . It’s given that $y$ is the height of the marble above the ground, in inches, and $x$ is the number of seconds after the marble started moving. It follows that the marble's height was $8$ inches above the ground $0$ seconds after it started moving. Therefore, the best interpretation of the y-intercept of the graph is that the marble’s height was $8$ inches above the ground when it started moving.

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.