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Analyzing Quadratic Functions Graphs: Vertex, AOS, and Opening Direction

Explore quadratic functions graphs with vertex form equations, identifying vertex, Axis of Symmetry, and direction of opening compared to the parent graph. Practice with sample equations.

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Analyzing Quadratic Functions Graphs: Vertex, AOS, and Opening Direction

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  1. 5.7 Analyzing graphs of Quadratic Functions

  2. Most basic quadratic function is • y = x2 • Axis of Symmetry is x = 0 • Vertex is (0, 0) • A family of graphs is a group of graphs that displays one or more similar characteristics! • y = x2 is called a parent graph

  3. Vertex Form y = a(x – h)2 + k • Vertex: (h, k) • Axis of symmetry: x = h • a is positive: opens up, a is negative: opens down • Narrower than y = x2 if |a| > 1, Wider than y = x2 if |a| < 1 • h moves graph left and right • - h moves right • + h moves left • k moves graph up or down • - k moves down • + k moves up

  4. Identify the vertex, AOS, and direction of opening. State whether it will be narrower or wider than the parent graph • y = -6(x + 2)2 – 1 • y = (x - 3)2 + 5 • y = 6(x - 1)2 – 4 • y = - (x + 7)2

  5. Graph after identifying the vertex, AOS, and direction of opening. Make a table to find additional points. y = 4(x+3)2 + 1

  6. y = -(x - 5)2 – 3

  7. y = ¼ (x - 2)2 + 4

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