Problem 88 - Algebra and Trigonometry

Question

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.

Step-by-Step Solution

Answer

Yes, the statement makes sense as the vertex of a parabola is indeed the point where it intersects its axis of symmetry.

Step 1: Understanding the definition of a parabola

A parabola is a curve where any point is at an equal distance from a fixed point called the focus and a fixed straight line called the directrix.

Step 2: Understanding the definition of axis of symmetry and vertex

The axis of symmetry of a parabola is a vertical line that divides the parabola into two identical halves. The vertex of the parabola is the point where the parabola makes its sharpest turn; it lies on the axis of symmetry.

Step 3: Evaluate the statement

Given the definitions in the previous steps, it's accurate to say that the vertex of a parabola is the point where the parabola intersects its axis of symmetry. This is because the vertex, being the point of maximum or minimum of the curve, is always located on this line of symmetry.