1. Content and Language
Integrated
Learning

2. Quadratic functions OBJECTIVES:
to arouse interest and curiosity showing images and introducing real problems involving quadratic functions.
- to know quadratic functions
Content
Images and real problems involving quadratic functions.
Language
The basic vocabulary to describe and define the quadratic functions
Keywords:
Increasing, decreasing, function and graph, to sketch a graph, parabola, roots, x and y axes, points of intersection, x-intercepts, y-intercept, irrational numbers, domain, range, maximum value (“n” shaped), minimum value (“u” shaped), vertex point, vertical line of symmetry, inequalities signs, to flip the inequality sign.
Study Skills and Strategies
Matching, completing activities
watching a video.

3. Images and real problems involving quadratic functions
Galileo proved that the trajectory of a projectile travelling through a non resisting medium is a parabola (1608)
A projectile is an object upon which the only force is gravity. A vertical force does not effect a horizontal motion. The result of a vertical force acting upon a horizontally moving object is to cause the object to deviate from its otherwise linear path

4. Parabolic shapes

5. Quadratic functions OBJECTIVES: - to know quadratic functions
- to sketch the graph of a quadratic functions with Geogebra
- construction of a parabola as a locus with Geogebra
Content
definition of a quadratic function and its graph
Language
Keywords, Present tenses, Conditionals type 0 and type 1, Imperatives, relative pronouns
Study Skills and Strategies
CAS (Geogebra) , class discussion
Activity 2.2.1: Definition of quadratic function:
The general form of a quadratic function is , where a, b and c are constant values ( ) and the highest power of x is 2. The graph of a quadratic function is called a parabola.

6. Sketching a quadratic graph with Geogebra

7. Parabola as a locus
Activity: construction of a parabola as a locus with Geogebra
Instructions to sketch the graph of a parabola as a locus with Geogebra:
Plot a straight line d, called “directrix”
Plot a point F which doesn’t lie on d, called “focus”
Plot a point Q on d
Plot the axis a of the line segment FQ
Plot the straight line b through Q and perpendicular to d
Plot the point P, intersection of a and b
Plot the locus of P with respect to Q on d
The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus.

8. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus.

9. Quadratic inequalities
OBJECTIVES: - to find any points of intersection between a quadratic function and a linear one
- to find the values of x for which f (x) < 0 or f (x) > 0
- to solve quadratic inequalities
Content
Any points of intersection between a quadratic function and a linear one; the values of x for which f (x) < 0 or f (x) > 0; quadratic inequalities.
Language
Key words, Present tenses, Conditionals type 0 and type 1
Study Skills and Strategies
working in pairs, problem solving

10. Real life problems OBJECTIVES: - to solve real-life problems Content
Language
Language involved in the given problems: Present Simple Tense, Conditionals Type 0 and Type 1, key words
Study Skills and Strategies
Cooperative learning

11. Real Life problems
A farmer has 16 metres of fencing with which to make a rectangular enclosure for sheep.
If one side of the enclosure is x metres long, show that the area A is given by
Draw the graph of A(x) in the domain . Use your graph to estimate:
The area of the enclosure when x = 2.5
The maximum possible area and the value of x when this occurs
The two values of x for which the area is 12 m2.
Jenny fires a scale model of a TV talent show presenter horizzontally with a velocity of 100 ms-1 from 1.5m above the ground.
How long does it take to hit the ground, and how far does it travel?
Assume the model acts as a particle, the ground is horizontal and there is no air resistance.

12. Real-life Problem
Draw the graph of the function y=6x- x² in the domain 0 ≤ x ≤ 6.
Y is the height, in metres, reached by a golf ball from the time it was hit (x=0) to the time it hits the ground (x=6). If each unit on the x-axis represents 1 second and each unit on the y-axis represents 5 metres, use your graph to estimate:
the greatest height reached by the golf ball
the height of the golf ball after 1.5 seconds

13. How to sketch the graph Y=0 C.E. 0 ≤ x ≤ 6 Y=x²-6x
Y= 6x-x² x²= x(x-6)=0
x₁= x₂=6
Xv= -b/2a= 6/2= 3
Yv=6(3) – (3)²= 9

14. Parabola’s graph

15. Process 1.Estimate the greatest height reached by the golf ball:
Y= x5m= 45 m
2. Estimate the hight of the golf ball after 1.5 seconds:
Y= 6(1.5) – (1.5)²= 6.75
Hight: 6.75x5m= 33.75m

16. Classwork OBJECTIVES: to evaluate students’ knowledge and skills
Content
Written classwork about quadratic functions
Language
All the language learned
Study Skills and Strategies
Each student must work individually

17. Self assessment 0 = totally disagree 1 = rather agree
2 = agree = totally agree 1 2 3
I’ve improved since the last self-assessment
I applied consistently
I have been interested in my studies
I have set goals that I then reached
I have studied with perseverance and diligence
I think I have made good progress in this period
I better understand my strengths and weaknesses
I know what I have to concentrate on for the review
I know what I need to do to improve