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Chapter 3: Problem 88

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I like to think of a parabola's vertex as the point where it intersects its axis of symmetry.

Short Answer

Expert verified
The statement makes sense. While phrasing could be slightly adjusted, the claim that the vertex of a parabola is located along the axis of symmetry is accurate.

Step by step solution

01

Definition of Vertex

The vertex of a parabola is the point at which the parabola makes its sharpest turn; it lies halfway between the focus and the directrix. It is also the maximum or minimum point of the parabola, depending on whether the parabola opens upwards/downwards or leftwards/rightwards.
02

Definition of Axis of Symmetry

The axis of symmetry of a parabola is the vertical or horizontal line that passes through the vertex, dividing the parabola into two perfectly symmetrical halves.
03

Interpreting the Statement

The statement claims that the vertex is the point where a parabola intersects its axis of symmetry. Given our definitions, this statement 'makes sense'. The vertex is indeed along the axis of symmetry. However, it might be more accurate to say that the axis of symmetry passes through the vertex, rather than the parabola intersects its axis of symmetry at the vertex.

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