Answer: Choice B
- vertex = (3, -4)
- y intercept = (0, 5)
- x intercepts = (1, 0) and (5, 0)
- axis of symmetry: x = 3
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Explanation:
The vertex is the lowest point for parabolas that open upward like this. The lowest point is (3, -4). If the parabola is flipped upside down, then the vertex would be the highest point.
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The y intercept is where the graph crosses the y axis. For any function, it will have at most one y intercept (some don't have any at all but the most you can have is 1 y intercept). The graph crosses the vertical y axis at (0,5). We can say in short "the y intercept is 5". The y intercept always occurs when x = 0.
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On the flip side, the x intercept always occurs when y = 0. This is where the graph crosses or touches the x axis. We have two such locations of (1,0) and (5,0). In short, we could say "the x intercepts are 1 and 5". The term "root" is another word we could use in place for "x intercept". Unlike the y intercept, we can have as many x intercepts as we want.
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The axis of symmetry is the vertical line through the parabola. It is the x coordinate of the vertex. So it's not a coincidence that the vertex is at (3,-4) and the axis of symmetry is x = 3, with those '3's repeated twice.
