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Vertex Form and Parabola Transformations

Algebra and Graphs Vertex Form and Parabola Transformations

🎬 Video Tutorial

(0:01) Vertex Form of Quadratic Equations: The vertex form is $y = a(x – h)^2 + k$, where $(h, k)$ is the vertex of the parabola and $a \neq 0$. For example, in $y = 0.5 (x – 2)^2 – 3$, the vertex is $(2, -3)$.
(0:14) Vertex as Turning Point: The vertex $(h, k)$ is the highest or lowest point. If $a > 0$, the parabola has a minimum at $x = h$ (opens upwards). If $a < 0$, it has a maximum at $x = h$ (opens downwards).
(1:28) Horizontal and Vertical Shifts: Changing $h$ shifts the parabola horizontally (left or right), and changing $k$ shifts it vertically (up or down). As long as $a$ remains the same, the shape of the parabola remains consistent.

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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.

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