Graph \( y=-2|x-3|+6 \). List the \( x \)-and \( y \)-intercept(s), if any. B. There are no \( x \)-intercepts. List the \( y \)-intercept(s). Select the correct choice below and, if necessary, fill in the an A. The y-intercept(s) of the graph is (are) \( \square \). (Type an ordered pair. Use a comma to separate answers as needed.)

To graph the function \( y = -2|x-3| + 6 \) and find the intercepts, we can follow these steps: 1. **Identify the vertex of the absolute value function**: The expression \( |x-3| \) has a vertex at \( x = 3 \). At this point, we can find the corresponding \( y \)-value: \[ y = -2|3-3| + 6 = -2(0) + 6 = 6. \] So, the vertex of the graph is at the point \( (3, 6) \). 2. **Determine the direction of the graph**: Since the coefficient of the absolute value is negative (-2), the graph opens downwards. 3. **Find the intercepts**: - **Y-intercept**: To find the y-intercept, set \( x = 0 \): \[ y = -2|0-3| + 6 = -2(3) + 6 = -6 + 6 = 0. \] Thus, the y-intercept is at the point \( (0, 0) \). - **X-intercepts**: To find the x-intercepts, set \( y = 0 \): \[ 0 = -2|x-3| + 6. \] Rearranging gives: \[ -2|x-3| = -6 \implies |x-3| = 3. \] This absolute value equation gives us two cases: 1. \( x - 3 = 3 \) which leads to \( x = 6 \). 2. \( x - 3 = -3 \) which leads to \( x = 0 \). Therefore, the x-intercepts are at the points \( (6, 0) \) and \( (0, 0) \). 4. **Summary of intercepts**: - The x-intercepts are \( (6, 0) \) and \( (0, 0) \). - The y-intercept is \( (0, 0) \). Since the problem states that there are no x-intercepts, it seems there might be a misunderstanding. However, based on our calculations, we found that the x-intercepts are indeed \( (6, 0) \) and \( (0, 0) \). ### Final Answer: A. The y-intercept(s) of the graph is (are) \( (0, 0) \).