[size=150][b]Topic : Effects of the Parameters/Values of a, h, and k on the graph of f(x)= a ( x - h)[sup]2[/sup] + k[/b] [br][/size][size=150][br][b]Grade Level The Topic is Taught : Grade 9 and Part in Grade 10[br][/b][br][b]Grade 9 MELC : Q1 _ Week 8[/b][br] Analyze the effects of changing the values of a , h, and k in the equation f(x) = a ( x - h)[sup]2[/sup] + k of the quadratic function on its graph.[br][br][b]Grade 10 MELC : Q1_ Week 1[/b][br] Understand , describe and interpret the graphs of polynomial function[br][br][b]How the Task will be Done[/b][br][br] This applet contains the graph of f(x) = a ( x - h)[sup]2[/sup]+ k and three sliders namely a, h and k. The three sliders will be used to help the learners visualize, analyze and state the relationship between the parameters/values of a , h and k and the graph of the function f(x) = a ( x - h)[sup]2[/sup]+ k[br]The graph also contains a point with coordinates. This point will be used to help the learners explain why the vertex is the highest or lowest point of the parabola.[br] This lesson can be used for online platforms if the learners have gadgets that can be downloaded with GeoGebra Application. In the face to face class, this can be used through a power point presentation via projector or a big screen Television.[br][br][b]Objectives : [/b][br][br] At the end of the lesson, with the aid of this applet, the learners are expected to:[br][br] 1. describe the graph of f(x) = a ( x - h)[sup]2[/sup]+ k in relation to the parameters/values of a.[br][br] 2. identify the location of the vertex of the graph of f(x) = a ( x - h)[sup]2[/sup]+ k in the Cartesian Plane  and in the graph itself based on the parameters/values of a, h and k.[br] [br] 3. explain how the minimum/maximum value of the graph of f(x) = a ( x - h)[sup]2[/sup]+ k can be  determined even without plotting of points.[/size]

1. On this applet is shown the graph of f(x) = a (x - h)[sup]2[/sup] + k. We call it the parabola. Now, look at the trend of the parabola as we change the value of a in the equation f(x) = a (x - h)[sup]2[/sup] + k. What do you notice? how will you describe the trend of the graph when a is less than zero ( -a)? when a = 0 ? when a is greater than zero ( +a)?[br][br]2. Why is it that when a = 0, the graph becomes a straight line?[br][br]3. Look at the value of a again in f(x) = a (x - h)[sup]2[/sup] + k, what do you notice about the size of the opening of the parabola as we change the value of a? How will you state the relationship between the size of the opening of the parabola and the value of a in f(x) = a (x - h)[sup]2[/sup] + k?[br][br]4. Use the sliders h and k. The values shown in the sliders are the values of h and k in the equation of the function being formed as changes made in the sliders. By just looking at the equation f(x) = a (x - h)[sup]2[/sup] + k, how will you determine the coordintes of the vertex of the parabola?[br][br]5. How will you describe the vertex in realtion to the trend/direction of the opening of the parabola and when will it happen in relation to the values of a in f(x) = a (x - h)[sup]2[/sup] + k?[br][br]6. With the aid of dragging a point on a graph with its coordintes shown, why is it that when a is less than zero, the vertex becomes the highest point and when a is greater than zero , the vertex becomes the lowest point? ( Hint :Use the realtionship between the value of x and the value of f(x). In the coordinates of the point on a graph of f(x), the first coordinte is the value of x while the second coordinte is the value of f(x) at the given value of x.)[br][br]7. How will you descrbe the value of the function f(x) = a (x - h)[sup]2[/sup] + k at its turning point (vertex) in relation  to the value of a?[br][br]8. How will you determine the maximum/minimum value of the graph of f(x) = a (x - h)[sup]2[/sup] + k even without  plotting of points?[br][br]9. How will you state now the relationship between the parameters/values of a,h and k and trend of the graph of f(x) = a (x - h)[sup]2[/sup] + k ?[br][br][br]Prepared by:[br][br]   JERRY M. MARAVILLA[br]  Vinisitahan National High School[br]   [br][br]