[list][*]Subject: Mathematics[br][/*][*]Class: IX B (profile, specialization natural sciences)[br][/*][*]Duration: 50 minutes[br][/*][*]ICTs: [i]PowerPoint presentations, computer, projector.[br][/i][i]ex. computer teacher projector, computers for students etc ...[/i][/*][/list]

[i]The graph function of the second degree.[/i]

[i][list][*]The recognition of the correspondence between the shape and position of the graph representation of the function of the second degree, coefficient values [b]a[/b] and discriminant[math]\Delta[/math];[/*][*]Graphical representation of a function of grade II[/*][*]Use of graphics to optimize reading and solving practical problems.[br][/*][/list][/i]

[b][i]-[/i][/b] to determine and discuss the intersections of a parabola with the axes depending on the sign of the discriminant[math]\Delta[/math]; [br]- discuss about graph shape and extreme value; [br]- write parabola vertex coordinates and establish minimum or maximum of a quadratic function.[br]

[b][i]Didactic methods and procedures[/i][/b] [br]-solving, discovery, modeling mathematical, exercise method. [br][br][i][b]Lesson times:[br][br][/b][/i][u] I) Introduction and organization of lesson (5 min.)[br][/u] The teacher presents the lesson theme and tell students that they will discover the properties of second degree function using computers and software GeoGebra. With projector shows the application "relative positions of a parabola - graph function Grade II" and how to use them.[br][br][u]II) Verification of prior learning (15 min.)[br][/u] Questions: - How are the intersection between graph and axes?[br][math]G_f\cap Ox=A\left(x_0,0\right)[/math] and [math]G_f\cap Oy=B\left(0,f\left(0\right)\right)[/math] [br]- How do we solve an equation of the second degree? What does discriminant [math]\Delta=b^2-4ac[/math] and how it will influence the intersection of the graph with x-axis? E.g,[math]f:\mathbb{R}\longrightarrow\mathbb{R},f\left(x\right)=x^2+x-6[/math][br]- How we deduced that the function of the second degree admits extreme value and how is it calculated? From the canonical form of function result that we have an extreme value (minimum if a <0, max if a> 0), equal to [math]-\frac{\Delta}{4a}[/math][br]- Examples: Write the canonical form and deduce the extreme value functions [math]f:\mathbb{R}\longrightarrow\mathbb{R}[/math][br][br]a) [math]f\left(x\right)=x^2-2x+7=...=\left(x-1\right)^2+6\ge6,\forall x\in\mathbb{R}[/math] [br][br]b) [math]f\left(x\right)=-x^2-4x+5=...=-\left(x+2\right)^2+9\le9,\forall x\in\mathbb{R}[/math][br][br][u]III) Learning of new knowledge (10 min.)[br][/u] Students study positions and graph shape using the interactive chart "The relative positions of a parabola -Second degree function graph". They will change the values of coefficient a and [math]\Delta[/math] observing and discussing the number of points of intersection with the horizontal axis and orientation parabola branches. They study all 6 possible combinations and organize the results, students write down the conclusions on notebooks next to graphs.[br][br][u]IV) The deepening of new knowledge (15 min.)[/u] [br]Create values table and draw on the notebooks graphs of the following functions[math]f:\mathbb{R}\longrightarrow\mathbb{R}[/math]. Discuss results by discriminant [math]\Delta[/math] and the dominant factor a: [br]a) [math]f\left(x\right)=x^2-3x+2[/math][br][br]b) [math]f\left(x\right)=4x^2+4x+1[/math][br][br]c) [math]f\left(x\right)=-x^2+x-1[/math][br][br][u]V) Review and ensure the transfer (5 min.)[br][/u] Students will write functions in input bar of GeoGebra Graph Calculator and compare them with those graphs above. They will communicate availability of this software adapted to mobile phones and will be invited to use personal phones. Then they will get home theme selection of exercises and problems from textbook.

[i][i]Quadratic function Graphical View: [url=https://ggbm.at/KKEYRDUg]https://ggbm.at/KKEYRDUg[/url][/i][/i]

[list][*]GeoGebra will use graphics manipulation and detection of the extent of the intrinsic properties of second degree function and the way in which the coefficients affecting the graphical representation.[/*][*]material will be prepared for the event of absence of the Internet and download / stream.[br][/*][*]possibly students will study GeoGebra site in previous ICT lesson to accommodate with platform and will find that the software is available on mobile.[/*][/list]