IM Alg2.2.6 Lesson: Different Forms
Which one doesn’t belong?
A: [math]y=\left(x+4\right)\left(x-6\right)[/math][br]B: [math]y=2x^2-8x-24[/math][br]C: [math]y=x^2+5x-25[/math][br]D: [math]y=x^3+3x^2-10x-24[/math]
[size=150]Earlier, we learned we can make a box from a piece of paper by cutting squares of side length [math]x[/math] from each corner and then folding up the sides. Let’s say we now have a piece of paper that is 8.5 inches by 14 inches. The volume [math]V[/math], in cubic inches, of the box is a function of the side length [math]x[/math] where [math]V\left(x\right)=\left(14-2x\right)\left(8.5-2x\right)\left(x\right)[/math].[br][/size][br]Identify the degree and leading term of the polynomial. Explain or show your reasoning.
Without graphing, what can you say about the horizontal and vertical intercepts of the graph of [math]V[/math]? [br]
Do these points make sense in this situation?
Use the distributive property to show that each pair of expressions is equivalent.
[math]\left(x+2\right)\left(x+4\right)[/math] and [math]x^2+6x+8[/math]
[math]\left(x+6\right)\left(x+-5\right)[/math] and [math]x^2+x-30[/math]
[math]\left(x^2+10x+7\right)\left(2x-1\right)[/math] and [math]2x^3+19x^2+4x-7[/math]
[math]\left(4x^3-8\right)\left(x^2+3\right)[/math] and [math]4x^5+12x^3-8x^2-24[/math]
Write a pair of expressions that each have 2 or 3 terms, and trade them with your partner. Multiply the expressions they gave you.[br]
[center][/center][size=150]Let [math]f\left(x\right)=\left(x-2\right)\left(x+3\right)\left(x-7\right)[/math] and[math]g\left(x\right)=\frac{1}{2}\left(x-2\right)\left(x+3\right)\left(x-7\right)[/math][/size][br][br]Use the applet below to explore both functions in the same window of [math]-10\le x\le10[/math] and [math]-100\le y\le100[/math]. [br]Describe how the two graphs are the same and how they are different.[br]
What degree do these polynomials have? Rewrite each expression in standard form to check.[br]
Let [math]h\left(x\right)=\left(3x-6\right)\left(x+3\right)\left(x-7\right)[/math]. What do you think the graph of [math]y=h\left(x\right)[/math] will look like compared to [math]y=f\left(x\right)[/math]? [br]Use the applet above to check your prediction.[br]
[size=150]Here are the graphs of two polynomial functions, [math]f[/math] and [math]g[/math]. We know that [math]g\left(x\right)=k\cdot f\left(x\right)[/math].[/size][br][img]data:image/png;base64,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[/img][br]Why do the two graphs have different vertical intercepts but the same horizontal intercepts?
What is the value of [math]k[/math]?[br]
IM Alg2.2.6 Practice: Different Forms
[math]f\left(x\right)=\left(x+3\right)\left(x-4\right)[/math] and [math]g\left(x\right)=\frac{1}{3}\left(x+3\right)\left(x-4\right)[/math]. The graphs of each are shown here.[br][img]data:image/png;base64,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[/img][br]Which graph represents which polynomial function? Explain how you know.[br]
For each polynomial function, rewrite the polynomial in standard form. Then state its degree and constant term.
[math]f\left(x\right)=\left(x+1\right)\left(x+3\right)\left(x-4\right)[/math]
[math]g\left(x\right)=3\left(x+1\right)\left(x+3\right)\left(x-4\right)[/math]
[size=150]Tyler incorrectly says that the constant term of [math](x+4)(x-4)[/math] is zero.[/size][br][br]What is the correct constant term?[br]
What is Tyler’s mistake? Explain your reasoning.[br]
Which of these standard form equations is equivalent to [math]\left(x+1\right)\left(x-2\right)\left(x+4\right)\left(3x+7\right)[/math]?
Select [b]all [/b]polynomial expressions that are equivalent to [math]5x^3+7x-4x^2+5[/math].
Select [b]all [/b]the points which are relative minimums of this graph of a polynomial function.[br][br][img]data:image/png;base64,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[/img]
What are the [math]x[/math]-intercepts of the graph of [math]y=\left(3x+8\right)\left(5x-3\right)\left(x-1\right)[/math]?