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]
Close

Information: IM Alg1.6.15 Lesson: Vertex Form