IM Alg1.6.17 Lesson: Changing the Vertex

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[/img][br][br][size=150]Here are graphs representing the functions [math]f[/math] and [math]g[/math], given by [math]f\left(x\right)=x\left(x+6\right)[/math] and [math]g\left(x\right)=x\left(x+6\right)+4[/math].[/size][br][br]Which graph represents each function? Explain how you know.[br]
Where does the graph of [math]f[/math] meet the [math]x[/math]-axis? Explain how you know.[br]
[size=150]How would you change the equation [math]y=x^2[/math] so that the vertex of the graph of the new equation is located at the following coordinates and the graph opens as described?[/size][br][br][math](0,11)[/math], opens up
[math](7,11)[/math], opens up
[math](7,\text{-}3)[/math], opens down
Use graphing technology to verify your predictions. Adjust your equations if necessary.
[size=150]Kiran graphed the equation [math]y=x^2+1[/math] and noticed that the vertex is at [math]\left(0,1\right)[/math]. He changed the equation to [math]y=\left(x-3\right)^2+1[/math] and saw that the graph shifted 3 units to the right and the vertex is now at [math]\left(3,1\right)[/math].[br][br]Next, he graphed the equation [math]y=x^2+2x+1[/math], observed that the vertex is at [math]\left(-1,0\right)[/math]. Kiran thought, “If I change the squared term [math]x^2[/math] to [math]\left(x-5\right)^2[/math], the graph will move 5 units to the right and the vertex will be at [math]\left(4,0\right)[/math].”[/size][br][br]Do you agree with Kiran? Explain or show your reasoning.
[size=150]Mai is learning to create computer animation by programming. In one part of her animation, she uses a quadratic function to show the path of the main character, an animated peanut, jumping over a wall.[br][br]Mai uses the equation [math]y=-0.1\left(x-h\right)^2+k[/math] to represent the path of the jump. [math]y[/math] represents the height of the peanut as a function of the horizontal distance it travels [math]x[/math]. On the screen, the base of the wall is located at [math]\left(22,0\right)[/math], with the top of the wall at [math]\left(22,4.5\right)[/math].[/size][br][size=150][br]The dashed curve in the picture shows the graph of one equation Mai tried, where the peanut fails to make it over the wall.[/size][br][br][img]data:image/png;base64,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[/img][br][br]What are the values of [math]k[/math] and [math]h[/math] in this equation?[br]
This applet is programmed to use Mai’s equation. Experiment with the applet to find an equation to get the peanut over the wall, and keep it on the screen. Be prepared to explain your reasoning.
Do you see 2 “eyes” and a smiling “mouth” on the graph?
[img]data:image/png;base64,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[/img][br][br]The 3 arcs on the graph all represent quadratic functions that were initially defined by [math]y=x^2[/math], but whose equations were later modified.[br][br]Write equations to represent each curve in the smiley face.[br]
Use this graphing technology to check your work.
What domain is used for each function to create this graph?[br]

IM Alg1.6.17 Practice: Changing the Vertex

Here the graph of quadratic function f.
[img]data:image/png;base64,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[/img][br][size=150]Andre uses the expression [math]\left(x-5\right)^2+7[/math] to define [math]f[/math].[br]Noah uses the expression [math]\left(x+5\right)^2-7[/math] to define [math]f[/math].[/size][br][br]Do you agree with either of them? Explain your reasoning.
[size=150]Here are the graphs of [math]y=x^2[/math], [math]y=x^2-5[/math], and [math]y=\left(x+2\right)^2-8[/math].[/size][br][br][img]data:image/png;base64,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[/img][br][br]How do the 3 graphs compare?
How does the -5 in [math]x^2-5[/math] affect the graph?[br]
How does the +2 and the -8 in [math]\left(x+2\right)^2-8[/math] affect the graph?[br]
[size=150]Which equation represents the graph of [math]y=x^2+2x-3[/math] moved 3 units to the left?[/size]
[size=150]Select [b]all[/b] the equations with a graph whose vertex has [i]both[/i] a positive [math]x[/math]- and a positive [math]y[/math]-coordinate.[/size]
[size=150]The height in feet of a soccer ball is modeled by the equation [math]g\left(t\right)=2+50t-16t^2[/math], where time [math]t[/math] is measured in seconds after it was kicked.[/size][br][br]How far above the ground was the ball when kicked?[br]
What was the initial upward velocity of the ball?[br]
Why is the coefficient of the squared term negative?[br]
[size=150]What is the vertex of the graph of the function [math]f[/math] defined by [math]f\left(x\right)=-\left(x-3\right)^2+6[/math]?[/size][br]
Identify the [math]y[/math]-intercept and one other point of the graph of this function.[br]
Sketch the graph of f.
At 6:00 a.m., Lin began hiking. At noon, she had hiked 12 miles.
[size=150]At 4:00 p.m., Lin finished hiking with a total trip of 26 miles.[br][/size][br]During which time interval was Lin hiking faster? Explain how you know. 
Kiran bought a smoothie every day for a week.
[size=150]Smoothies cost $3 each. The amount of money he spends, in dollars, is a function of the number of days of buying smoothies.[/size][br][br]Sketch a graph of this function. Be sure to label the axes.[br]
Describe the domain and range of this function.[br]
A deposit of $500 has been made in an interest-bearing account. No withdrawals or other deposits (aside from earned interest) are made for 5 years.
[size=150]Write an expression to represent the account balance for each of the following situations.[/size][br][br]6.5% interest calculated monthly
6.5% interest calculated every two months
6.5% interest calculated quarterly
6.5% interest calculated semi-annually
[size=150]Function [math]h[/math] is defined by [math]h\left(x\right)=5x+7[/math] and function [math]k[/math] is defined by [math]k\left(x\right)=\left(1,005\right)^x[/math].[/size][br][br]Complete the table with values of [math]h(x)[/math] and [math]k\left(x\right)[/math]. When necessary, round to 2 decimal places.[br]
Which function do you think [i]eventually[/i] grows faster? Explain your reasoning.[br]
Use graphing technology to verify your answer to the previous question.

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