IM Alg1.6.15 Lesson: Vertex Form

What do you notice? What do you wonder?
[table][tr][td]Set 1:[/td][td]Set 2:[/td][/tr][tr][td][math]f(x)=x^2+4x[/math][br][br][math]g(x)=x(x+4)[/math][br][br][math]h(x)=(x+2)^2-4[/math][/td][td][math]p(x)=\text-x^2+6x-5[/math][br][br][math]\\q(x)=(5-x)(x-1)[/math][br][br][math]r(x)=\text-1(x-3)^2+4[/math][/td][/tr][/table]
Here are two sets of equations for quadratic functions you saw earlier.
[size=150]In each set, the expressions that define the output are equivalent. [/size][br][br][table][tr][td]Set 1:[/td][td]Set 2:[/td][/tr][tr][td][math]f(x)=x^2+4x[/math][br][br][math]g(x)=x(x+4)[/math][br][br][math]h(x)=(x+2)^2-4[/math][/td][td][math]p(x)=\text-x^2+6x-5[/math][br][br][math]\\q(x)=(5-x)(x-1)[/math][br][br][math]r(x)=\text-1(x-3)^2+4[/math][br][br][/td][/tr][/table][br][br][size=150]The expression that defines [math]h[/math] is written in [b]vertex form[/b]. We can show that it is equivalent to the expression defining [math]f[/math] by expanding the expression:[/size][br][br][center][math]\displaystyle \begin {align} (x+2)^2-4 &=(x+2)(x+2)-4\\ &=x^2+2x+2x+4-4\\ &=x^2+4x\\ \end{align}[/math][/center][br]Show that the expressions defining [math]r[/math] and [math]p[/math] are equivalent.
[size=150]Here are graphs representing the quadratic functions.[/size][br][br][table][tr][td]Graph of [math]h[/math] [/td][td]Graph of [math]r[/math] [br][/td][/tr][tr][td][img]data:image/png;base64,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[/img][/td][td][img]data:image/png;base64,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[/img][br][/td][/tr][/table][br]Why do you think expressions such as those defining [math]h[/math] and [math]r[/math] are said to be written in vertex form?[br]
Using graphing technology, graph y=x².
[size=150]Then, add different numbers to [math]x[/math] before it is squared (for example, [math]y=\left(x+4\right)^2[/math], [math]y=\left(x-3\right)^2[/math]) and observe how the graph changes. [/size][br]Record your observations.[br]
[size=150]Graph [math]y=\left(x-1\right)^2[/math]. Then, experiment with each of the following changes to the function and see how they affect the graph and the vertex:[/size][br][br][list][*]Adding different constant terms to [math]\left(x-1\right)^2[/math] (for example: [math]\left(x-1\right)^2+5[/math], [math]\left(x-1\right)^2-9[/math]).[br][/*][*]Multiplying [math]\left(x-1\right)^2[/math] by different coefficients (for example: [math]y=3\left(x-1\right)^2[/math], [math]y=-2\left(x-1\right)^2[/math]).[/*][/list]
Without graphing, predict the coordinates of the vertex of the graphs of these quadratic functions, and predict whether the graph opens up or opens down. Ignore the last row until the next question.
Use graphing technology to check your predictions. If they are incorrect, revise them. Then, complete the last row of the table.
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[/img][br][br]What is the vertex of this graph?[br]
Find a quadratic equation whose graph has the same vertex and adjust it, if needed, so that it has the graph provided.[br]

IM Alg1.6.15 Practice: Vertex Form

[size=150]Select [b]all[/b] of the quadratic expressions in vertex form.[/size]
Here are two equations. One defines function m and the other defines function p. Show that the expressions defining m and p are equivalent.
What is the vertex of the graph of [math]m[/math]? Explain how you know.[br]
What are the [math]x[/math]-intercepts of the graph of [math]p[/math]? Explain how you know.[br]
For each equation, write the coordinates of the vertex of the graph that represents the equation.
[math]y=\left(x-3\right)^{^2}+5[/math]
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[/img][br][br]Which equation is represented by the graph?[br]
[math]y=\left(x+7\right)^{^2}+3[/math]
[math]y=\left(x-4\right)^{^2}[/math]
[math]y=x^2-1[/math]
[math]y=2\left(x+1\right)^{^2}-5[/math]
[math]y=-2\left(x+1\right)^{^2}-5[/math]
[size=150]For each function, write the coordinates of the vertex of its graph and tell whether the graph opens up or down.[/size]
Here is a graph that represents y=x².
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[/img][br][br]Describe what would happen to the graph if the original equation were modified as follows:[br][br][math]y=-x^2[/math]
[math]y=3x^2[/math]
[math]y=x^2+6[/math]
Sketch the graph of the equation y=-3x²+6 on the same coordinate plane as y=x².
Here are four graphs. Match each graph with a quadratic equation that it represents.
Noah is going to put $2,000 in a savings account.
[size=150]He plans on putting the money in an account and leaving it there for 5 years. He can put the money in an account that pays 1% interest monthly, an account that pays 6% interest every six months, or an account that pays 12% interest annually.[/size][br][br]Which account will give him the most money in his account at the end of the 5 years?
The table shows some input and output values of function f.
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[/img][br][br]Describe a possible rule for the function by using words or by writing an equation.[br]

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