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Unit 1B quadratics

Unit 1B quadratics. Day 3. 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. Vertex Form. Tells us the direction in which the parabola opens. Provide the coordinates of the vertex: (h, k).

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Unit 1B quadratics

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  1. Unit 1Bquadratics Day 3

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

  3. 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

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

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

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

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

  8. 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)

  9. 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

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

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

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

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

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

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

  16. 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.

  17. MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k. f(x) DomainThe domain of a function is the set of all possible input values, x, which yield an output x y RangeThe range of a function is the corresponding set of output values, y. 17

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

  19. Find the domain and range of the quadratic Function. f(x) = x2 + 1 Domain: all real numbers Range: y ≥ 1 (the set of all real numbers greater than or equal to 1) 19

  20. Domain of all parabolas is all real numbers… 20

  21. 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

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

  23. Assignment • 3.2 Practice WS (#1-12 all)

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