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📐 Mathematics  ·  Straight Lines  ·  JEE

The vertex of parabola y = (x-2)² + 3 is:

Answer: (2,3).

  • A (2,3)
  • B (-2,3)
  • C (2,-3)
  • D (3,2)

Correct answer: A. (2,3)

Explanation: Vertex form y = (x-h)² + k has vertex at (h,k) = (2,3).

Slope as Rise over Runxy(x₁,y₁)(x₂,y₂)run = x₂−x₁rise = y₂−y₁m = rise/run = (y₂−y₁)/(x₂−x₁) = tanθ

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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