Vertex Form and Parabola Transformations

Learn how to use vertex form of quadratic equations, y=a(xh)2+ky = a(x−h)^2 + k, to find the vertex and shift a parabola. Let’s get started! 🚀

Vertex Form and Parabola Transformations - introduction visual

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Vertex form of quadratic equation y = a(x - h)² + k, showing the vertex at point (h,k) on a graph of a parabola.Vertex form of quadratic equation y = a(x - h)² + k showing how horizontal (h) and vertical (k) shifts affect a parabola's position on a graph.Graph showing transformation of the quadratic equation from y = -2x² with vertex (0,0) to y = -2(x+2)² + 3 with vertex (-2,3), shifting the parabola.

🛎️ Vertex Form of a Quadratic

  • The vertex form is y = a(x − h)² + k, and the vertex is (h, k).
  • For example, in y = 2(x + 3)² − 1, the vertex is (−3, −1).

🛎️ What Do h and k Mean?

  • h moves the graph left or right.
  • k moves the graph up or down.

🛎️ Shifting a Parabola Using Vertex Form

  • Start with y = 2x², which has its vertex at (0,0).
  • Moving the vertex 3 left and 1 down gives the new graph y = 2(x + 3)² − 1.

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Vertex form and parabola transformations

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