How to induce a parabola? What is a parabola? How do square alignments tie? Lesson “Function y=ax2, її graph and power Parabola mind y ax2 bx c
Summary of the lesson in algebra for the 8th grade of the middle sacred lighting school
Lesson topic: Function
meta lesson:
· Lighting: change the understanding of the quadratic function to the form (reverse the graphs of the functions and ), show the formula for the significance of the coordinates of the vertex of the parabola (learn to put this formula into practice); to formulate the assignment of the power of the quadratic function behind the graph (change the axis of symmetry, the coordinates of the parabola vertex, the coordinates of the point of the crossbar of the graph with the coordinate axes).
· Developing: a development of a mathematical movie, in a correct way, consistently and rationally express your thoughts; development of the skill of correct recording of a mathematical text for additional symbols and designations; development of analytical thought; development of the cognitive activity of the students through smart analysis, systematization and aggregation of the material.
· Vikhovna: the cultivation of self-reliance, the consideration of listening to others, the formation of accuracy and respect for writing mathematical language
lesson type: development of new material
Training methods:
narrowly-reproductive, inductively-heuristic.
Wimogi to know that vmin uchniv
know that such a quadratic function of the mind, the formula for the significance of the coordinates of the vertex of the parabola; you know the coordinates of the vertex of the parabola, the coordinates of the point of the crossbar of the graph of the function with the coordinate axes, behind the graph of the function to signify the power of the quadratic function.
Settlement:
lesson plan
I. Organizational moment (1-2 minutes)
II. Actualization of knowledge (XV 10)
III. Presentation of new material (XV 15)
IV. Confirmation of new material (XV 12)
V. Pіdbitya pіdbagіv (3 xv)
VI. Head of home (2 xv)
Hid lesson
I. Organizational moment
Welcoming, re-checking daily, picking up zoshitiv.
II. Actualization of knowledge
teacher: At this year's lesson, we will learn a new topic: "Function" Ale, for the cob, we repeat earlier in the material.
Frontal experience:
1) What is called a quadratic function? (Function, de tasks dіysnі numbers, , The reference is changed, is called a quadratic function.)
2) What is the graph of a quadratic function? (The graph of a quadratic function is a parabola.)
3) What are zero quadratic functions? (Zeros of a quadratic function is a value, for which it turns to zero.)
4) Override the power of the function. (The value of the function is positive when i reaches zero when ; the graph of the function is symmetrical around the axis of the ordinate; when the function grows, when it changes.)
5) Override the power of the function. (So , then the function gets positive values at , so , then the function gets see the meaning at , the value of the function is equal to 0; the parabola is symmetrical along the ordinate axis; yakso , then the function grows at i falls off at , yakso , then the function grows at , falls off at .)
III. Presentation of new material
teacher: Let's get down to the development of new material Vіdkriyte zoshiti, write down the number and topic of the lesson. Give respect to the doshka.
Recording on the dosh: Number.
Function.
teacher: There are two graphs of functions on the board. The first graph, and the other. Let's try to match them.
You know the power of the function. On the basis of these principles, and on the basis of our schedules, we can call the power of the function.
Otzhe, how do you think, in view of what is the root of the parabola straight off?
Learn: Directly, both parabolas are dependent on the coefficient.
Teacher: Absolutely correct. It can also be said that in both parabolas there are all symmetry. The first graph of the function, what is the main symmetry?
Learn: A parabola has a mind of all symmetry and all ordinates.
Teacher: Correctly. And what about all the symmetry of the parabola
Learn: The axis of symmetry of the parabola is a line, yak to pass through the top of the parabola, parallel to the axis of ordinates.
teacher: That's right Otzhe, all the symmetry of the graph of the function is called a straight line, which passes through the top of the parabola, parallel to the y-axis.
And the top of the parabola is the whole point with the coordinates. The stench follows this formula:
Write the formula in a box and circle it in a box.
Recording on doshtsi and zoshita
The coordinates of the vertices of the parabola.
teacher: Now, schob was zrozumіlіshe, we can look at the butt
butt 1: Find the coordinates of the vertex of the parabola.
Solution: Behind the formula
teacher: As we have already appointed, all symmetry to pass through the top of the parabola Marvel at the board. Baptize this little one at the zoshity.
Recording on doshtsi and zoshita:
Teacher: On armchairs: - alignment of the axis of symmetry of the parabola with the top at the point, de abscissa of the top of the parabola.
Let's look at an example.
Example 2: Behind the graph of the function is the alignment of the axis of symmetry of the parabola.
Alignment of the axis of symmetry can be seen: also the alignment of the axis of symmetry of this parabola.
Note: - Equalization of the axis of symmetry.
IV. Confirmation of new material
teacher: On the doshtsi written down the task, yakі nebhіdno vyrіshiti in the class
Recording on the dosh: № 609(3), 612(1), 613(3)
Teacher: Ale, on the back of the head, we will untie the butt not from the handkerchief. Virishuvatememo beat the dosk.
Example 1: Know the coordinates of the vertex of the parabola
Solution: Behind the formula
Suggestion: coordinates of the vertex of the parabola.
Example 2: Find the coordinate point of the parabola 
with coordinate axes.
Solution: 1) From the top:
Tobto. 
Behind Viet's theorem:
Crosspoints along the abscissa (1; 0) and (2; 0).
2) From the beginning:
A speck of peretina from all ordinates (0; 2).
Value: (1; 0), (2; 0), (0; 2) - coordinate point of the line with the coordinate axes.
Summary of the lesson in algebra for the 8th grade of the middle school
Lesson topic: Function
meta lesson:
· Lighting: change the understanding of the quadratic function to the form (reverse the graphs of the functions and ), show the formula for the significance of the coordinates of the vertex of the parabola (learn to put this formula into practice); to formulate the assignment of the power of the quadratic function behind the graph (change the axis of symmetry, the coordinates of the parabola vertex, the coordinates of the point of the crossbar of the graph with the coordinate axes).
· Developing: a development of a mathematical movie, in a correct way, consistently and rationally express your thoughts; development of the skill of correct recording of a mathematical text for additional symbols and designations; development of analytical thought; development of the cognitive activity of the students through smart analysis, systematization and aggregation of the material.
· Vikhovna: the cultivation of self-reliance, the consideration of listening to others, the formation of accuracy and respect for writing mathematical language
lesson type: development of new material
Training methods:
narrowly-reproductive, inductively-heuristic.
Wimogi to know that vmin uchniv
know that such a quadratic function of the mind, the formula for the significance of the coordinates of the vertex of the parabola; you know the coordinates of the vertex of the parabola, the coordinates of the point of the crossbar of the graph of the function with the coordinate axes, behind the graph of the function to signify the power of the quadratic function.
Settlement:
lesson plan
I. Organizational moment (1-2 minutes)
II. Actualization of knowledge (XV 10)
III. Presentation of new material (XV 15)
IV. Confirmation of new material (XV 12)
V. Pіdbitya pіdbagіv (3 xv)
VI. Head of home (2 xv)
Hid lesson
I. Organizational moment
Welcoming, re-checking daily, picking up zoshitiv.
II. Actualization of knowledge
teacher: At this year's lesson, we will learn a new topic: "Function" Ale, for the cob, we repeat earlier in the material.
Frontal experience:
1) What is called a quadratic function? (Function , where given effective numbers, , Correct change, is called a quadratic function.)
2) What is the graph of a quadratic function? (The graph of a quadratic function is a parabola.)
3) What are zero quadratic functions? (Zeros of a quadratic function is a value, for which it turns to zero.)
4) Override the power of the function. (The value of the function is positive when i reaches zero when ; the graph of the function is symmetrical around the axis of the ordinate; when the function grows, when it changes.)
5) Override the power of the function. (Also, then the function gains positive values at , but , then the function gains negative values at , the value of the function is more stable 0 only; at .)
III. Presentation of new material
teacher: Let's get down to the development of new material Vіdkriyte zoshiti, write down the number and topic of the lesson. Give respect to the doshka.
Recording on the dosh: Number.
Function.
teacher: There are two graphs of functions on the board. The first graph, and the other. Let's try to match them.
You know the power of the function. On the basis of these principles, and on the basis of our schedules, we can call the power of the function.
Otzhe, how do you think, in view of what is the root of the parabola straight off?
Learn: Directly, both parabolas are dependent on the coefficient.
Teacher: Absolutely correct. It can also be said that in both parabolas there are all symmetry. The first graph of the function, what is the main symmetry?
Learn: A parabola has a mind of all symmetry and all ordinates.
Teacher: Correctly. And what about all the symmetry of the parabola
Learn: The axis of symmetry of the parabola is a line, yak to pass through the top of the parabola, parallel to the axis of ordinates.
teacher: That's right Otzhe, all the symmetry of the graph of the function is called a straight line, which passes through the top of the parabola, parallel to the y-axis.
And the top of the parabola is the whole point with the coordinates. The stench follows this formula:
Write the formula in a box and circle it in a box.
Recording on doshtsi and zoshita
The coordinates of the vertices of the parabola.
teacher: Now, schob was zrozumіlіshe, we can look at the butt
butt 1: Find the coordinates of the vertex of the parabola. 
.
Solution: Behind the formula
maybe:
teacher: As we have already appointed, all symmetry to pass through the top of the parabola Marvel at the board. Baptize this little one at the zoshity.
Recording on doshtsi and zoshita:
Teacher: On armchairs: - alignment of the axis of symmetry of the parabola with the top at the point, de abscissa of the top of the parabola.
Let's look at an example.
Example 2: Behind the graph of the function is the alignment of the axis of symmetry of the parabola.
Alignment of the axis of symmetry can be seen: also the alignment of the axis of symmetry of this parabola.
Note: - Equalization of the axis of symmetry.
IV. Confirmation of new material
teacher: On the doshtsi written down the task, yakі nebhіdno vyrіshiti in the class
Recording on the dosh: № 609(3), 612(1), 613(3)
Teacher: Ale, on the back of the head, we will untie the butt not from the handkerchief. Virishuvatememo beat the dosk.
Example 1: Know the coordinates of the vertex of the parabola
Solution: Behind the formula
maybe:
Suggestion: coordinates of the vertex of the parabola.
Example 2: Find the coordinate point of the parabola 
with coordinate axes.
Solution: 1) From the top:
Tobto. 
Behind Viet's theorem:
Crosspoints along the abscissa (1; 0) and (2; 0).
2) From the beginning:
VI. Homework
Teacher: On the doshtsi it is written the task of home. Record yoga with students.
Entry on the doshtі that in students: §38, no. 609(2), 612(2), 613(2).
Literature
1. Alimov Sh.A. Algebra Grade 8
2. Sarantsev G.I. Methodology for teaching mathematics in middle school
3. Mishin V.I. Private methodology for teaching mathematics in middle school
A filthy reader to present the truth, a good one to read and get it.
O.Disterweg
teacher: Netikova Margarita Anatoliivna, teacher of mathematics, School No. 471 of the Viborsky district of St. Petersburg.
Theme of the lesson: “Graphic functiony= ax 2 »
lesson type: a lesson in learning new knowledge.
Target: Learn to learn how to schedule a function y= ax 2 .
Manager:
Initial: form a parabola y= ax 2 and install the regularity between the graph of the function y= ax 2
that coefficient a.
Developing: development of cognitive wisdom, analytical and poignant thought, mathematical literacy, building capacity and workmanship.
Whip out: vyhovannya interest in the subject, accuracy, vidpovidalnosti, excitability to oneself and others.
Planned results:
Subject: follow the formula to designate directly the length of the parabola and be її for the additional table.
Features: remember your point of view and practice in pairs, among the collective.
Metasubjects: to plan and evaluate the process and the result of your activity, to process information.
Pedagogical technologies: elements of the problematic and viperedzhuyuchy navchannya.
Ownership: interactive whiteboard, computer, handouts.
1. The formula for the roots of a square equalization and the expansion of a square trinomial into factors.
2. Short algebraic fractions.
3. Power and function schedule y= ax 2 , staleness of the straight line of the parabola, її “stretching” and “squeezing” of the y-axis of the y-axis of the coefficient a.
Lesson structure.
1. Organizational part.
2.Updating knowledge:
Revising housekeeper
Sleeping robot with a ready-made armchair
3. Independent work
4. Explanation of the new material
Preparation before the development of new material (solution of a problem situation)
First acquisition of new knowledge
5.Fixed
Zastosuvannya knowledge and wisdom in a new situation.
6.Introducing the bag to the lesson.
7. Homework.
8. Reflection to the lesson.
Technological map for an algebra lesson in grade 9 on the topic: “Function graphy=
ax 2
»
| Etapi lesson | Stage manager | The duty of the teacher | Diyalnistst uchniv | UUD |
| 1. Organizational part 1 whilina | Creation of a working mindset on the cob of the lesson | Hanging out with the teachings review your preparation before the lesson, designate days, write down the date. | Get ready to work at the lesson, read the readers | Regulatory: organization of primary activities. |
| 2. Actualization of knowledge 4 hwilini | Revisit the study of homework, repeat and learn from past lessons the material and create mind for a successful study of self-sufficient work. | Selecting scores from six students (selection of two from the skin row) for rechecking homework for assessment (Supplement 1), then practice with the class on the interactive board (Supplement 2). | Six scientists ask for a review of homework, then they give food for frontal education (Supplement 2). | Knowing: given knowledge of the system. Communications: vminnya listen to the thoughts of the restless. Regulatory: evaluating the results of their activities. Features: assessment of the level of mastering the material. |
| 3. Independent work 10 whilin | Reverse the multiplication of the quadratic trinomial, fasten the fractions of algebra and describe the acts of the power of functions for the її schedule. | Distribute cards to students with individual differentiation tasks (Appendix 3). the leaves for the cherry. | Conquering an independent work, independently stealing the balance of folding is right for the balls. | Knowing: Features: evaluating the level of mastering the material and its capabilities. |
| 4. Explanation of the new material Preparing for the production of new material First acquisition of new knowledge | Creation of a pleasant environment for getting out of a problem situation, accepting that comprehension of new material, independent I come to the right visnovku | Sincerely, you will be the schedule of the function y= x 2 (The charts were prompted ahead of time on three boards). Name the main power functions: 3. Vertex coordinates 5. Intermittent monotony Why in to this particular type good coefficient at x 2 ? On the butt of a square trinomial, they made it, which is neobov'yazkovo. How can you get a sign? Bring examples. How to look at the parabola with other coefficients, you will have to find out for yourself. The best way to win schos-tse vіdkriti most. D.Poya Divided into three teams (in rows), we choose captains, so they go up to the board. The task for the teams is written on three boards, the sign is broken! Induce graphs of functions in one coordinate system 1 team: a) y \u003d x 2 b) y \u003d 2x 2 c) y \u003d x 2 2 team: a) y \u003d - x 2 b) y \u003d -2x 2 c) y \u003d - x 2 3 team: a) y \u003d x 2 b) y \u003d 4x 2 c) y \u003d -x 2 Zavdannya vikonano! (Appendix 4). Know the functions that seem to be the same in power. The captains are happy with their teams. Why lie down? And why do these parabolas still wind up and why? Why lay the “tovshchina” of the parabola? In what way to lie straight down the head of a parabola? Mentally, we call the schedule a) “let go”. Show your own gum: if you pull it out, it becomes thinner. Otzhe, graph b) deducting the expansion of the outward graph of the axis of ordinates. How is schedule c) removed? That means, at x 2 you can stand whether it is some kind of coefficient, some kind of injecting the configuration of the parabola. Axis i theme of our lesson sound like this: "Schedule functiony= ax 2 » | 1. R 4. Hills uphill 5. Change to (- It grows on, and the growth of the function grows on the interval. The values of this function cover the entire positive part of the action axis, there are no more important points to zero, and there is no largest value. On slide 15, the power of the function y = ax 2 is described, which is also negative. It is important that the graph also pass through the cob of coordinates, but all points, ie, lie at the lower surface. The symmetry of the graph along the axis is indicated, and the opposite values of the argument are given equal values of the function. The function grows for the interim, changes. The value of this function lies at the interval, zero points are out of place, and there is no smallest value.
Let’s take a closer look at the characteristics, on slide 16 it will be shown that the parabola needles are straightened down, and uphill - at. The parabola is symmetrical about the axis, and the top of the parabola is ruffled at the point of the crossbar from the top. The vertex of the parabola y=ax 2 is the cob of coordinates. Also, an important visnovo about the transformation of the parabola is displayed on slide 17. On the new presentation of the variant of the transformation of the graph of a quadratic function. It is noted that the graph of the function y=ax 2 is transformed on a symmetrical display of the graph like an axis. It is also possible to compress or stretch the graphics freely. On the rest of the slide, there are some more important notes about the transformation of the graphics of the function. Visnovkas are made about those that the graph of the function should be symmetrical to the transformations of the axis. And the graph of the function will appear with the force or expansion of the output graph in the axis. At the same time, the rise of the axis is at times guarded by the fall, if. Squeeze to the axis in 1/a times the schedule is settled at the times.
The presentation “Function y=ax 2 , її schedule and power” can be taken as a teacher as a learning aid in the lesson of algebra. Also, this helper kindly reveals the topic, giving the ruined understanding of the subject, so it can be proponated for independent education by teachings. Also, this material will help the teacher to give an explanation for the hour of distance learning. Share with friends or save for yourself:
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