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Quadratic Functions in Vertex Form

Learn about quadratic functions in vertex form, their properties, and how they compare to the parent function. Understand how different values of "a" affect the graph's shape, direction, and width. Explore examples and discover how shifts in "h" and "k" impact the function's vertex, axis of symmetry, domain, and range.

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Quadratic Functions in Vertex Form

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  1. Quadratic Functions in Vertex Form

  2. Parent function • f(x) = x2 • This is the simplest quadratic function. We will use this one as a model by which to compare all other quadratic functions we will examine.

  3. Vertex Form • f(x) = a(x - h)2 + k • y = a(x - h)2 + k Example: f(x) = 4(x - 3)2+5

  4. Vertex Form • y = a(x - h)2 + k • if a>0, the graph opens up • if a<0, the graph opens down • if |a|>1, the graph is narrower than the parent function • if |a|<1, the graph is wider than the parent function • if |a|=1, the graph is the same as the parent function

  5. Vertex Form y = a(x - h)2 + k Vertex = (h, k) Axis of Symmetry x = h h makes the graph shift left and right (-h=left; +h=right) k makes the graph shift up and down (-k=down; +k=up)

  6. Example 1 • y = (x - 1)2 + 2 • Vertex • Axis of Symmetry • Opens? • Narrows, Widens, or no Change?? • Shifts??? • Domain • Range

  7. Example 2 • f(x) = -1/3(x + 1)2 + 3 • Vertex • Axis of Symmetry • Opens? • Narrows, Widens, or no Change??? • Shifts??? • Domain • Range

  8. Example 3 • f(x) = 2x2 - 3 • Vertex • Axis of Symmetry • Opens? • Narrows, Widens, or no Change??? • Shifts??? • Domain • Range

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