Topicme408391fd85dd353_1528449000663_0Topic

The vertex formvertex formvertex form and the standard formstandard formstandard form of the quadratic functionquadratic functionquadratic function

Levelme408391fd85dd353_1528449084556_0Level

Third

Core curriculumme408391fd85dd353_1528449076687_0Core curriculum

V. Functions. The student:

7) sketches the graph of the quadratic functionquadratic functionquadratic function given by a formula,

8) interprets the coefficients found in the quadratic function formula in the standard, vertex and factored form (if any),

9) determines the quadratic function formula based on the information about this function or its graph.

Timingme408391fd85dd353_1528449068082_0Timing

45 minutes

General objectiveme408391fd85dd353_1528449523725_0General objective

Interpreting and handling information presented in the text, both mathematical and popular science, as well as in the form of graphs, diagrams, tables.

Specific objectivesme408391fd85dd353_1528449552113_0Specific objectives

1) Communicating in English, developing mathematical and basic scientific‑technical and IT competence, forming of learning skills.

2) Conversion of the standard formstandard formstandard form into the vertex formvertex formvertex form of the quadratic functionquadratic functionquadratic function.

3) Conversion of the vertex form into the standard form of the quadratic function.

Learning outcomesme408391fd85dd353_1528450430307_0Learning outcomes

The student:

- Describes the quadratic functionquadratic functionquadratic function using the standard and vertex formvertex formvertex form.

- Converts the standard formstandard formstandard form of the quadratic function into the vertex form and reversely.

Methodsme408391fd85dd353_1528449534267_0Methods

1) Situational analysis.

2) Mind maps.

Forms of workme408391fd85dd353_1528449514617_0Forms of work

1) Individual work.

2) Work in small groups.

Lesson stages

Introductionme408391fd85dd353_1528450127855_0Introduction

The students work in small groups. Their task is to systematize the previously acquired knowledge about the quadratic functionquadratic functionquadratic function presented in the vertex formvertex formvertex form and in the standard formstandard formstandard form.

They present collected information as a mind map.

Procedureme408391fd85dd353_1528446435040_0Procedure

The teacher informs the students that the aim of the lesson is to develop the competence of converting the vertex formvertex formvertex form into the standard formstandard formstandard form and reversely - the standard form into the vertex form.

The students work in small groups and analyse the slideshow presenting the conversion of the vertex form into the standard form. They draw a conclusion.

[Slideshow 1]

Conclusion
To change the formula of the quadratic function, written in the vertex form, into the standard form, one should simplify the formula by multiplying out and combining like terms.me408391fd85dd353_1527752263647_0To change the formula of the quadratic function, written in the vertex form, into the standard form, one should simplify the formula by multiplying out and combining like terms.

The students apply the acquired knowledge in exercises.

Task
Present the quadratic function $y={\left(x-\frac{1}{3}\right)}^2+4$ in the standard form.

Task
Present the quadratic function $y=-\frac{2}{5}{\left(x+5\right)}^2-15$ in the standard formstandard formstandard form. Sketch the graph of that function. Read out from the graph the range of the function.

The students work independently and analyse the slideshow presenting the conversion of the standard form into the vertex formvertex formvertex form. They formulate a conclusion.

[Slideshow 2]

Conclusion
To convert the formula of the quadratic function written in the standard form into the vertex form one should apply a method of completing the square of the sum or difference of two terms.me408391fd85dd353_1527752256679_0To convert the formula of the quadratic function written in the standard form into the vertex form one should apply a method of completing the square of the sum or difference of two terms.

The students apply the acquired knowledge in exercises.

Task
Present the quadratic function $f\left(x\right)=x^2-6x-2$ in the vertex formvertex formvertex form. Find the equation of the symmetry axis of the parabolasymmetry axis of the parabolasymmetry axis of the parabola which is the graph of that function.

Task
Present the function $f\left(x\right)=2x^2-4x+6$ in the vertex form. Find the coordinates of the vertex of the parabolacoordinates of the vertex of the parabolacoordinates of the vertex of the parabola which is the graph of that function. Sketch the graph.

Work in groups. Each group has a task to prepare one exercise. The solution of the exercise requires changing the formula of a quadratic functionquadratic functionquadratic function. Students exchange exercises and present solutions.

An example of an exercise prepared by one of the groups.

Find the coefficients $b$ and $c$ of the quadratic function $f\left(x\right)=x^2+bx+c$ given the coordinates of the vertex $W(10,-3)$ of the parabolaparabolaparabola which is the graph of this function.

An extra task
Determine a number of solutions of the equation $0.5x^2-4x=m-6$ depending on the parameter $m$.

Lesson summaryme408391fd85dd353_1528450119332_0Lesson summary

Students perform consolidating exercises. Then they summarize together the lesson, formulating conclusions to be remembered:

- To change the formula of the quadratic functionquadratic functionquadratic function written in the vertex formvertex formvertex form into the standard formstandard formstandard form one should simplify the formula by multiplying out and combining like terms.

- To convert the formula of the quadratic function written in the standard form into the vertex form one should apply a method of completing the square of the sum or difference of two terms.

Selected words and expressions used in the lesson plan

coordinates of the vertex of the parabolacoordinates of the vertex of the parabolacoordinates of the vertex of the parabola

numerical coefficientsnumerical coefficientsnumerical coefficients

parabolaparabolaparabola

quadratic functionquadratic functionquadratic function

standard formstandard formstandard form

symmetry axis of the parabolasymmetry axis of the parabolasymmetry axis of the parabola

vertex formvertex formvertex form

vertex of the parabolavertex of the parabolavertex of the parabola