ACTIVITY 8 vertex of a parabola
Activity description identifies the student and the vertex of a parabola graphically. Now find the vertex with two different methods completing the trinomial perfect square and by formula. Using GeoGebra graph the function and point to the vertex and the methods studied in class will find the vertex by the method indicated. The following activities. Development of the activity
The vertex of a parabola is represented by V (h, k), and can be obtained algebraically and graphically.
Algebraically
know that quadratic functions are written in the general form y = ax ² + bx + c can be easily obtained by the method of completing the square trinomial perfect place to express it in standard form y = a (xh) ² + k . Using Graphically
GeoGebra can graph a quadratic function and identify the vertex.
determines the vertex function f (x) = 2x ² - 8x + 5 by the method of completing the square and then check your results with the help of GeoGebra noting the location of the vertex.
If we know that h = (- b/2a) and k = c - (b ² / 4a) can apply these formulas to get the vertex.
determines the vertex of f (x) = x ² - 2x + 3, if we know that c =______. =_____, b =______ Then we apply the formulas:
V (- b/2a, c - (b ² / 4a)
V (- _____/2_______, _______ - (_____²/ 4_______))
V (-______, 3-______) V
(______, 2)
Determines the top of the parables by the method of completing the square and check your result in GeoGebra.
a) f (x) = x ² - 10x - 3
b) g (x) = 4x ² - 12 x + 5
c) h (x) = 2x ² - 6 x + 3
determines the vertex of the parabolas using the second method and check the result in GeoGebra pointing your result.
a) f (x) = 3x ² - 2x + 1
b) g (x) = 27x ² + 12 x - 7
c) h (x) = x ² - 16 x - 63
ACTIVITY 9
Description of Activity
The student will practice everything learned during the teaching sequence solving the following activities: Development
activity determines the characteristics of each of the following quadratic functions, finding solutions, the behavior of the graphs comparing with f (x) = x ² with the help of GeoGebra. For each of the equations fill out a questionnaire as follows: Ratio
cuadrático_______________
Towards the end where they open the concavity es_______________________________
ramas_____________________
It has a maximum or mÃnimo_________________
The maximum or minimum value is______________________
axis equation symmetry is x = h, then the axis of symmetry is x =__________
The value that corresponds to the maximum or minimum does not supply the value of k.
This is f (h) = k so it _________. Vertex is V
(____,_____)
a) f (x) = 2x ² + 8x - 5
b) g (x) = 1/4x ² + 8 x + 3
c) h (x) = x ² + 4 x
d) f (x) = 2x ² - 8x
e) g (x) =-x ² - 6 x +8
f) h (x) = 2x ² - 12 x + 19
g) f (x) = ¾ x ² - 6x + 2
h) g (x) =-3x ² - 18 x + 26
i) h (x) = 4x ² - 8 x - 7
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