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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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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