Provide an appropriate response.Explain why the vertex of a parabola must lie on its axis.

Question

What will be an ideal response?

Answer 1

Explanations will vary. One possibility: The vertex of a parabola must lie on its axis because, by definition, the axis is a line that intersects the vertex, dividing the parabola into two equal parts. For the parabola defined by the following function:

the vertex is at (h, k) and the vertical line x = h is the axis of the parabola. This vertical line includes all ordered pairs (h, y) and thus clearly includes (h, k).