Presentacion sobre funciones cuadraticas

Cuadraticas

1. Quadratic Graphs To see the equation of a quadratic function. To create graphs of quadratic functions. To know the name of this curve and its elements. *

2. Quadratic equations * A quadratic function always contains a term in x 2 . It can also contain terms in x or a constant. General equation : Make a table of values for y = x 2 with -2 < x < 2. Draw the curve X Y

3. * X -2 -1 1 2 Y 4 1 1 2

4. Example II * Make a table of values for y = - x 2 with -2 < x < 2. Draw the curve X Y

5. * X -2 -1 1 2 Y - 4 - 1 - 1 - 2

6. Using a table of values Plot the graph of y = x 2 – 3 for values of x between –3 and 3. We can use a table of values to generate coordinates that lie on the graph as follows: x y = x 2 – 3 –3 –2 –1 1 2 3 6 (–3, 6) 1 –2 –3 –2 1 6 (–2, 1) (–1, –2) (0, –3) (1, –2) (2, 1) (3, 6)

7. Using a table of values x y = x 2 – 3 –3 –2 –1 1 2 3 6 1 –2 –3 –2 1 6 The points given in the table are plotted … x –2 –1 –3 1 2 3 –1 –2 1 2 3 4 5 y y … and the points are then joined together with a smooth curve. The shape of this graph is called a parabola . It is characteristic of a quadratic function .

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9. * Interpretation of parameters a and c Use your GDC to draw graphs and complete: Which parameter tells that the parabola is happy (concave up) or sad (concave down) ? Which parameter tells the y-int in the graph? What is the value of the y-coordinate in the roots? How many roots can have a parabola?

10. * Finding the roots and y-int, from a quadratic functions

11. * Finding the coordinates of the vertex and the axis of symmetry

12. * Given y = x 2 + 6x – 7 , find: The coordinates of y-int (… , …) The roots x 1 = …. x 2 = ….. The equation of the axis of symmetry ……………….. The coordinates of the vertex (… , …) Draw the graph

13. We can express the quadratic function in three different ways: General or explicit form: f(x) = ax 2 + b x + c Factorise form : f(x)= a(x – x 1 )(x - x 2 ) Turning point form or vertex form: f(x)= a(x - x v ) 2 +y v x 1 x 2 (X v ,Y v )

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