Transfroming Quadratic Funct in SF to VF

Transforming Quadratic functions

1. 10th grade

2. Graphs a Quadratic Function 10th grade

3. Objectives 1. Graph a quadratic functions. 2. Identify the following using the graph of QF (a) domain; (b) range; (c) intercepts; (d) axis of symmetry; (e) vertex; (f) direction of the opening of the parabola. 3. Display active participation in answering the activity.

4. *How can quadratic functions in the form y = (x-h) 2 + k be graphed? Since the quadratic function is in its vertex form, the vertex can be easily identified . The vertex is represented by ( h,k ). The axis of symmetry is the value of h that is h=x . The x-intercept/s is solved by letting y=0 and the y-intercept by letting x=0.The domain is the set of all real numbers. The range is { y:y } if the graph opens upward while the range is { y:y } if the graph opens downward. The graph opens upward if the a≥0 while it opens downward if a≤0 .  

5. Graph of a Quadratic Functions Show the following: Domain Ra nge x- and y- intercepts Vertex Axis of symmetry Directio n of the opening of the parabola

6. Examples 1. +2 2. 3. 4. 5. 6.  

7. The effects of changing the values of a, h and k in the equation y = a(x – h)2 + k of a quadratic function on its graph.

8. FUNCTION A function is a correspondence between a first set called the domain , and a second set, called the range , such that each member of the domain corresponds to exactly one member of the range.

9. DOMAIN Correspondence RANGE

10. The Graph of Example:   Quadratic Function A quadratic function is a function that can be written in the form , where are real numbers and . The highest exponent of the variable is 2, hence it is called a second degree function. Its graph is a parabola.  

11. The Graph of Example: g   For For the parabola opens downward. The coefficient in makes the graph narrower or wider. This behavior of the graph is called stretching . If the graph of the parabola is narrower than the graph of If the graph of the parabola is wider than the graph of  

12. The Graph of Example:   The graph of If is positive , the graph of is shifted upwards units. If is negative , the graph of is shifted downwards units.  

13. The Graph of Examples:   The graph of has the same shape as the graph of - If is positive, the graph of is the graph of shifted units to the right. - If is negative, the graph of is the graph of shifted units to the left. The vertex of the graph is and its axis of symmetry is the vertical line  

14. The Graph of Examples:   The graph of The graph of  

15. The Graph of Examples:   The graph of If is positive , the graph of is shifted upwards units. If is negative , the graph of is shifted upwards units.