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Unit 1B quadratics Day 3

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Graphing a Quadratic Function EQ: How do we graph a quadratic function that is in vertex form? M2 Unit 1B: Day 3 Lesson 3.1B

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Vertex Form Tells us the direction in which the parabola opens Provide the coordinates of the vertex: (h, k) ** NOTE: Always change the sign of h

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4 First, we must be able to identify a, h, and k in each quadratic function. a = 2h = 3k = 1a = -1h = -2k = -4

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5 Name the vertex of each quadratic function and determine if the parabola opens up or down. a = -2h = 3k = 4a = 1h = -1k = 2 Vertex is (3,4) Parabola opens down Vertex is (-1,2) Parabola opens up Vertex is (-4,0) Parabola opens down Vertex is (0,0) Parabola opens up

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To find the y-intercept, substitute zero for each x in the equation Course 3 Y-intercept of a Quadratic Functions Find the y-intercept for 6 Example 3

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Y-intercept of a Quadratic Functions Find the y-intercept for 7 Example 4

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Find the y-intercept of the given Quadratic Functions The y-intercept is -14 or (0, -14) The y-intercept is 3 or (0, 3)

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In order to graph using vertex form: Find the axis of symmetry and sketch it. Find the vertex, then plot it. Find the y-intercept, then plot it and its “twin” or “mirror image” Find another point and its “mirror image” 9

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Extrema – y-coordinate of the vertex Maximum – the Vertex when the parabola opens down Minimum – the vertex when the parabola opens up minimum maximum 10

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Vertex: (1, 3) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Minimum at y = 3 11 h = 1k = 3a = 2 Opens UP Axis of symmetry: (0, 5) (3, 11)

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12 Vertex: (-1, -1) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Maximum at y = -1 h = -1k = -1a = -1 Opens DOWN Axis of symmetry: (0, -2) (1, -5)

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13 Vertex: (2, 0) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Minimum at y = 0 h = 2k = 0a = 1 Opens UP Axis of symmetry: (0, 4) (1, 1)

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14 Vertex: (-3, -2) Y-intercept: One more point: Graph the quadratic using the axis of symmetry and vertex. Maximum at y = -2 h = -3k = -2a = -1 Opens DOWN Axis of symmetry: (0, -11) (-2, -3)

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Ex7. How would you translate the graph of to produce the graph of ? *Focus on how the vertex shifts! Old vertex: (0, 0) New vertex: (-2, -1) Translate left 2 units and down 1 unit.

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9. How would you translate the graph of to produce the graph of ? Old vertex: (0, 0) New vertex: (1, 5) Translate right 1unit and up 5 units.

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Domain The domain of a function is the set of all possible input values, x, which yield an output f(x) 17 x y MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. Range The range of a function is the corresponding set of output values, y.

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Domain VS. Range Domain: (x – values) read domain from left to right Range: (y-values) read range from bottom to top

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Find the domain and range of the quadratic Function. f(x) = x 2 + 1 Domain: all real numbers Range: y ≥ 1 (the set of all real numbers greater than or equal to 1) 19

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Domain of all parabolas is all real numbers… 20

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Find the domain and range of the quadratic Function. f(x) = (x - 2) 2 + 5 Domain: all real numbers Range: y ≤ 5 (the set of all real numbers less than or equal to 5) 21

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Find the domain and range of the quadratic Function. f(x) = - (x + 2) 2 - 1 Domain: all real numbers Range: y ≥ -1 22

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Assignment 3.2 Practice WS (#1-12 all)

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