Brandon was asked to identify the relative maximum of the polynomial function h(x)

Question

. Which answer choice identifies the correct value(s)?
grid points (-1,-2) (0,2(1,0) (2,2) (3,2)
(1 point)
Responses

There is a relative maximum at x=0
.
There is a relative maximum at x equals 0 .

There is a relative maximum at x=2
.
There is a relative maximum at x equals 2 .

There is a relative minimum at x=1
.
There is a relative minimum at x equals 1 .

There is no relative maximum in this graph.

Answer 1

To identify the relative maximum of the polynomial function \( h(x) \) based on the provided grid points, we analyze the y-values at these x-values:

• At \( x = -1 \), \( h(-1) = -2 \)
• At \( x = 0 \), \( h(0) = 2 \)
• At \( x = 1 \), \( h(1) = 0 \)
• At \( x = 2 \), \( h(2) = 2 \)
• At \( x = 3 \), \( h(3) = 2 \)

The highest y-value occurs at \( x = 0 \), \( x = 2 \), and \( x = 3 \) where \( h(x) = 2 \).

Since both \( x = 2 \) and \( x = 3 \) yield the same y-value, these can also be considered as relative maximum points, along with \( x = 0 \).

From the options provided, the correct answers regarding maxima would be:

• There is a relative maximum at \( x = 0 \).
• There is a relative maximum at \( x = 2 \).
• There is a relative maximum at \( x = 3 \) (although this option is not provided).

If you are looking for just one answer based on the provided choices, then either "There is a relative maximum at \( x = 0 \)" or "There is a relative maximum at \( x = 2 \)" would be correct. However, if you must choose one, select one of those two depending on your priority.