4.  Standard Form  y = ax 2 + bx + c, where a ≠ 0  Examples › y = 3x 2 › y = x 2 + 9 › y = x 2 – x – 2 › y = - x 2 + 2x - 4

5. f(x) = x 2 or y = x 2

6.  Axis of symmetry › The fold or line that divides the parabola into two matching halves.  Vertex › The highest or lowest point of a parabola. › Maximum or Minimum

7. Domain Range  The domain is all possible input (or x) values. › For our quadratics, the domain will always be all real numbers.  The range is all output (or y) values. › For our quadratics, the range will always be one of the following formats  y > the y part of the vertex  y ≥ the y part of the vertex  y < the y part of the vertex  y ≤ the y part of the vertex

8. Vertex: (-2, 8) Axis of Symmetry: x = -2 Maximum Domain: All Real #’s Range: y ≤ 8

9.  a will determine whether there is a maximum or minimum value › If a > 0, then there is a minimum (parabola opens up) › If a < 0, then there is a maximum (parabola opens down)  a also determines the “steepness” of the quadratic function  Vertex: the vertex will be (0, c)

10. I created this power point using the 2010 version. If you are not using the 2010 version, you will need to go to my links and I have included all links under the heading Quadratics.

13.  Standard Form of a quadratic equation: ax 2 + bx + c = 0  Roots of the equation or zeros of the function › solutions of the quadratic equations › x-intercepts of the graph

14.  Zero-Product Property › For any real numbers a and b, if ab = 0, then a = 0 or b = 0. › Example: If (x+3)(x+2) = 0, then x+3 = 0 or x+2 = 0.  You can use the Zero-Product Property to solve quadratic equations of the form ax 2 +bx+C = 0 if that quadratic can be factored. Remember to solve a quadratic equation means the same as finding the x-intercepts on the graph.

15. I created this power point using the 2010 version. If you are not using the 2010 version, you will need to go to my links and I have included all links under the heading Quadratics.

16.  Turning x 2 + bx into a perfect-square trinomial  Why do this? › Really the only reason to do this is to help out when trying to find the vertex form of a quadratic function.

17. I created this power point using the 2010 version. If you are not using the 2010 version, you will need to go to my links and I have included all links under the heading Quadratics.

19. Factoring and Zero-Product Property Quadratic Formula  You should factor to solve a quadratic equation (find the x-intercepts) if the quadratic can be factored.  You are good at factoring.  You can use the quadratic formula to solve (find the x-intercepts) any quadratic equation.  You must memorize or at least know how to use the quadratic formula.

20. Practice Problems: Pages 571-572 #7-15, 29-34 I created this power point using the 2010 version. If you are not using the 2010 version, you will need to go to my links and I have included all links under the heading Quadratics.

22.  a in all forms will › Determine the “steepness” of the parabola › Determine whether the parabola opens up or down  i.e. whether there is a maximum or minimum value  c is the y-intercept: › (0, c) is the point where the parabola crosses the y-axis › not necessarily the vertex of the parabola.