Vertex Form and Parabola Transformations
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(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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