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Graphing Quadratic Functions: Vertex Form and Standard Form

Learn how to graph quadratic functions in vertex form and standard form, understand translations and axis of symmetry. Practice identifying even and odd functions. Solve problems involving vertices and points in the graph. Homework and guided practice included.

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Graphing Quadratic Functions: Vertex Form and Standard Form

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  1. Do Now 3/27/19 • Take out HW from last night. • Text p. 446, #20-44 evens • Copy HW in your planner. • Text p. 446, #6-12 evens, #58-62 evens • Puzzle Time 8.4 • In your notebook, write a quadratic function in vertex form and standard form whose graph has the given vertex and passes through the given point. Vertex; (-2,-4); passes through (-1, -6)

  2. On Your Own Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. Vertex; (-2,-4); passes through (-1, -6) y = -2(x + 2)2 –4 y = -2x2 - 8x - 12

  3. HomeworkText p. 446, #20-44 evens

  4. HomeworkText p. 446, #20-44 evens

  5. HomeworkText p. 446, #20-44 evens

  6. HomeworkText p. 446, #20-44 evens

  7. Learning Goal • SWBAT graph quadratic functions Learning Target • SWBAT practice graphing functions of the form f(x) = a(x – h)² + k

  8. Section 8.4 “Graphing f(x) = a(x – h)² + k” Vertex Form of a quadratic function is the form f(x) = a(x – h)2 + k, where a ≠ 0. The vertex of the graph of the function is (h, k) and the axis of symmetry is h.

  9. The Graph of f(x) = a(x – h)² When h > 0, the graph of ax2 is translated RIGHT h units. When h < 0, the graph of ax2 is translated LEFT h units.

  10. The Graph of f(x) = a(x – h)² + k When k > 0, the graph of ax2 is translated UP k units. When k < 0, the graph of ax2 is translated DOWN k units.

  11. Find the axis of symmetry and vertex of the graph of the function f(x) = a(x – h)2 + k Vertex: (h, k) Axis of Symmetry: x = h y = -6(x + 4)2 - 3 y = -4(x + 3)2 + 1 Axis of Symmetry: Axis of Symmetry: x = -4 x = -3 Vertex: Vertex: (-4, -3) (-3, 1)

  12. Graph: y = a(x – h)² + k. Compare to f(x) = x2 y = 3(x – 2)² – 1 y = 3(x - 2)² - 1 “Parent Quadratic Function” y = x² Axis of x = h symmetry: x = 2 Vertex: (h, k) (2, -1) 1 2 0 11 x-axis The graph of y is a vertical stretch by a factor of 3, a horizontal translation right 2 units and a vertical translation down 1 unit. y-axis

  13. On Your Own Graph the Following Functions. Compare to the graph of f(x) = x2. h(x) = 1/2(x + 4)2 - 2 h(x) = -(x – 2)2 The graph of h is a vertical shrink by a factor of 1/2, and a translation 3 units left and 2 units down of the graph of f. The graph of h is a horizontal translation 2 units right and a reflection in the x-axis of the graph of f.

  14. Write a quadratic function in vertex form AND standard form whose graph has the given vertex and passes through the given point. Vertex; (-5, 6); passes through (-3, 8) y = a(x - h)2 + k y = a(x + 5)2 + 6 8 = a(-3 + 5)2 + 6 8 = a(2)2 + 6 8 = 4a+ 6 y = 1/2(x + 5)2 + 6 2 = 4a y = 1/2x2 + 5x + 37/2 1/2 = a

  15. Identifying EVEN or ODD functions A function y = f(x) is... EVEN ODD when f(-x) = -f(x) when f(-x) = f(x) The graph is symmetric about the origin after reflections in the x-axis and then the y-axis. The graph is symmetric about the y-axis. EVEN means SAME ODD means OPPOSITE NEITHER means DIFFERENT (besides opposite) Khan Academy video tutorial

  16. Identifying EVEN or ODD functions Is the function EVEN, ODD, or NEITHER? ODD EVEN When f(-x) = -f(x) When f(-x) = f(x) f(x) = 2x f(x) = x2-2 f(-x) = 2(-x) f(-x) = (-x)2-2 Substitute -x Substitute -x f(-x) = -2x f(-x) = x2-2 Simplify Simplify f(-x) = -2x f(x) = 2x f(-x) = x2-2 f(x) = x2-2 Compare Compare OPPOSITE means ODD SAME means EVEN

  17. TRY IT OUT… Is the function EVEN, ODD, or NEITHER? f(x) = 4x2 f(x) = x2-2x+3 Substitute -x f(-x) = 4(-x)2 f(-x) = (-x)2-2(-x)+3 Substitute -x f(-x) = 4x2 f(-x) = x2+2x+3 Simplify Simplify f(-x) = 4x2 f(x) = 4x2 f(-x) = x2-2x+3 f(x) = x2+2x+3 Compare Compare SAME means EVEN DIFFERENT means NEITHER

  18. Guided Practice With your 2:00 partner, complete PuzzleTime worksheet 8.4 - Schoology

  19. Homework • Puzzle Time worksheet 8.4 • Text p. 446, #6-12 evens, #58-62 evens

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