In this activity, we will explore the use of sliders and how they affect the components of Quadratic functions. Furthermore, we will be exploring some the characteristics and components of Geogebra. It is your responsibility to learn and apply these Geogebra commands in the future.
[b]Step 1:[/b] In the input bar, type the letter "a", "h" and "k" --this should create 3 sliders[br][br][b]Step 2[/b]: In the input bar, type in the equation: [math]f\left(x\right)=a\left(x-h\right)^2+k[/math]
[b]Question 1[/b]: Explain the result of your graph
[b]Step 3[/b]: Set your sliders to the following: a = 1 , h = 0, k = 0
[b]Question 2[/b]: What is the vertex of the parabola of the graph with those slider values?[br][br][b]Question 3:[/b] Describe the characteristics of this parabola, i.e. vertex, orientation, zeros.
[b]Step 4[/b]: Move your sliders around ... Keep "a" at 1 and move the "h" slider, then move the "k" slider, then move the "a" slider. Play around with it and notice what happens each time you move the slider
[b]Question 4[/b]: Explain how each variable (a, h, k) affects the movement of the graph?
[b]Step 5[/b]: Now we want to change the characteristics of the slider...[br]a) Click on the 3 dots to the right of the slider and go to "settings". You should see[br]the settings window off to the right. Click on "slider" and change your settings to [br]the following: Min: -10, Max: 10, increment: .10[br]Then click the X to close that window.[br]Do this to all 3 sliders.
[b]Question 5[/b]: Explain what the .10 does in relation to the slider
[b]Question 6[/b]: Consider the function: [math]f\left(x\right)=x^2+6x+5[/math], graph this function in the input bar (in this form). [br]Then, create your "a" , "h" and "k" sliders and create the equivalent parabola as [math]f\left(x\right)=a\left(x-h\right)^2+k[/math]. You SHOULD NOT be doing any algebra, use the sliders to match the function.[br]Click on your second function, click on this icon "wheel" icon and change one of the colors of the function.
[b]PART 2[/b]: Now we are going to use the slider "a", "b" and "c". In your input bar, create 3 sliders (a, b and c) and type the function: [math]f\left(x\right)=ax^2+bx+c[/math] in the input bar.
[b]Question 7[/b]: Set your sliders to a = 1, b =4 c = 4[br][br]Explain what the characteristics of this parabola are.
[b] Question 8: [/b] Move all three sliders around and notice what each slider does to the graph.[br][br]a) What transformations does the "a" slider do?[br][br]b) What transformations does the "b" slider do?[br][br]c) What transformations does the "c" slider do?
[b]Question 9:[/b] Using your sliders, create a graph that has solutions as 2 and -4. State your "a", "b" and "c" values.
[b]Question 10:[/b] Using your sliders, create a parabola facing downwards that has one solution at x = 3. State your "a", "b", and "c" values
[b]Question 11[/b]: Consider the quadratic function that has the following points: (-2, 4), (-4, -4), (0, -4). Find the values of "a", "b" and "c" that creates the function that contains those points.
[b]Question 12[/b]: Consider the following graph that contains those points. . Find the equation of the parabola in Standard Form (that's the [math]ax^2+bx+c[/math] )form. [br]Put your equation in the input bar to check your work
[b]Question 13:[/b] On the graph below is an image of the Golden Gate bridge. Using your point tool [icon]/images/ggb/toolbar/mode_complexnumber.png[/icon] to[br]plot three to four points along the suspension cables of the bridge. Then create your equation [math]f\left(x\right)=ax^2+bx+c[/math] and the three sliders "a", "b" and "c" and see if you can create a mathematical model[br]to determine a function that can model the bridge.
State your equation that best matches the image.