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5.1graphquadratics

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  • what is the explanation and solution of the express y=3x2-4x+1 in the formula of the quadratic function and give the values of h and k
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5.1graphquadratics

  1. 1. Warm-up  Evaluate when x = -1, 0, and 2. 1. y = 2x2 - 3x + 5 2. y = 3(x - 7)2 - 6 3. y = -(x + 3)(2x - 7)
  2. 2. Graphing Quadratic Equations 5.1 p. 249
  3. 3. Quadratic Functions  A quadratic function has the form y = ax2 + bx + c.
  4. 4. Quadratic Functions  A quadratic function has the form y = ax2 + bx + c.  The graph of a quadratic is called a parabola.
  5. 5. Quadratic Functions  A quadratic function has the form y = ax2 + bx + c.  The graph of a quadratic is called a parabola.  The vertex is the lowest or highest point on the parabola.
  6. 6. Quadratic Functions  A quadratic function has the form y = ax2 + bx + c.  The graph of a quadratic is called a parabola.  The vertex is the lowest or highest point on the parabola.  The axis of symmetry is the vertical line going through the vertex.
  7. 7. Quadratic Functions  Graphing calculator: y=1/2x2 , y=x2 , y=2x2 , y=3x2
  8. 8. Quadratic Functions  The parabola opens up if a > 0.
  9. 9. Quadratic Functions  The parabola opens up if a > 0.  The parabola opens down if a < 0 (negative).
  10. 10. Quadratic Functions  The x-coordinate of the vertex is -b/2a.
  11. 11. Quadratic Functions  The axis of symmetry is the vertical line x = - b 2a
  12. 12. Quadratic Functions  The parabola is wider if a is a fraction.
  13. 13. Quadratic Functions  The parabola is wider if a is a fraction.  It is narrower if a is a whole number greater than 1.
  14. 14. EX: y = 2x2 - 8x + 6  Find the x-coordinate of the vertex.
  15. 15. EX: y = 2x2 - 8x + 6  Find the x-coordinate of the vertex.  Find the y-coordinate
  16. 16. EX: y = 2x2 - 8x + 6 1. Plot the vertex.
  17. 17. EX: y = 2x2 - 8x + 6 1. Plot the vertex. 2. Draw the axis of symmetry.
  18. 18. EX: y = 2x2 - 8x + 6 1. Plot the vertex. 2. Draw the axis of symmetry. 3. Plot 2 points on one side
  19. 19. EX: y = 2x2 - 8x + 6 1. Plot the vertex. 2. Draw the axis of symmetry. 3. Plot 2 points on one side, and mirror them on the other side.
  20. 20. EX: y = 2x2 - 8x + 6 1. Plot the vertex. 2. Draw the axis of symmetry. 3. Plot 2 points on one side, and mirror them on the other side. 4. Draw a parabola through the points.
  21. 21. Quadratic Functions  If the equation is in the form y=a(x-h)2 +k,  The vertex is at (h, k)  The axis of symmetry is at x = h.
  22. 22. Quadratic Functions  y = 2(x - 1)2 + 3 Right 1 Up 3 vertex

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