Question
What describes the graph of y = |x - 3| + 8?
a ‘V’ shaped graph with vertex at (3, 8), which opens up
a ‘V’ shaped graph with vertex at (8, -3), which opens down
a ‘V’ shaped graph with vertex at (8, 3), which opens down
a ‘V’ shaped graph with vertex at (-3, 8), which opens up
a ‘V’ shaped graph with vertex at (3, 8), which opens up
a ‘V’ shaped graph with vertex at (8, -3), which opens down
a ‘V’ shaped graph with vertex at (8, 3), which opens down
a ‘V’ shaped graph with vertex at (-3, 8), which opens up
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Answered by
GPT-4o mini
The equation \( y = |x - 3| + 8 \) describes a V-shaped graph. To analyze it:
1. The expression \( |x - 3| \) indicates that the vertex of the graph occurs at \( x = 3 \).
2. The term \( +8 \) shifts the entire graph vertically upwards by 8 units.
Thus, the vertex of the graph is located at \( (3, 8) \).
Since the absolute value function opens upwards, the graph will indeed be a 'V' shape that opens up.
Therefore, the correct description is:
**a ‘V’ shaped graph with vertex at (3, 8), which opens up.**
1. The expression \( |x - 3| \) indicates that the vertex of the graph occurs at \( x = 3 \).
2. The term \( +8 \) shifts the entire graph vertically upwards by 8 units.
Thus, the vertex of the graph is located at \( (3, 8) \).
Since the absolute value function opens upwards, the graph will indeed be a 'V' shape that opens up.
Therefore, the correct description is:
**a ‘V’ shaped graph with vertex at (3, 8), which opens up.**
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