Which must be true of a quadratic function whose vertex is the same as its y-intercept?

The y-intercept is the point where x = 0. If the vertex is the same point as the y-intercept, then the vertex has x-coordinate 0. A parabola’s axis of symmetry passes through its vertex and is vertical, so it must be x = 0. Whether the function has zero, one, or two x-intercepts depends on its shape and position, so those are not guaranteed.

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