[size=150]To write [math]11x^2+17x-10[/math] in factored form, Diego first listed pairs of factors of -10.[br][/size][br][math](\underline{\hspace{.25in}}+ 5)(\underline{\hspace{.25in}} + \text{-}2)[/math][br][math](\underline{\hspace{.25in}}+ 2)(\underline{\hspace{.25in}} + \text{-}5)[/math][br][math](\underline{\hspace{.25in}} + 10) (\underline{\hspace{.25in}} + \text{-}1)[/math][br][math](\underline{\hspace{.25in}} + 1) (\underline{\hspace{.25in}}+ \text{-}10)[/math][br][br][size=100]Use what Diego started to complete the rewriting.[/size]
How did you know you’ve found the right pair of expressions? What did you look for when trying out different possibilities?[br]
[size=150]To rewrite [math]4x^2-12x-7[/math] in factored form, Jada listed some pairs of factors of [math]4x^2[/math]:[br][/size][br][math](2x+ \underline{\hspace{.25in}})(2x + \underline{\hspace{.25in}})[/math][br][math](4x + \underline{\hspace{.25in}})(1x + \underline{\hspace{.25in}})[/math][br][size=100][br]Use what Jada started to rewrite [math]4x^2-12x-7[/math] in factored form.[/size]
[math]7x^2-22x+3=0[/math]
[size=150]Han is solving the equation [math]5x^2+13x-6=0[/math]. Here is his work:[/size][br][br][math]\begin{align} 5x^2+13x-6 &= 0 \\ (5x-2)(x+3) &= 0\\x=2 \quad &\text{ or }\quad x=\text-3 \end{align}[/math][br][br][size=100]Describe Han’s mistake. Then, find the correct solutions to the equation.[/size]
[size=150]A picture is 10 inches wide by 15 inches long. The area of the picture, including a frame that is [math]x[/math] inch thick, can be modeled by the function [math]A\left(x\right)=\left(2x+10\right)\left(2x+15\right)[/math].[br][/size][br][size=100]Use function notation to write a statement that means: the area of the picture, including a frame that is 2 inches thick, is 266 square inches.[/size]
What is the total area if the picture has a frame that is 4 inches thick?
[size=150]To solve the equation [math]0=4x^2-28x+39[/math], Elena uses technology to graph the function [math]f\left(x\right)=4x^2-28x+39[/math]. She finds that the graph crosses the [math]x[/math]-axis at [math]\left(1.919,0\right)[/math] and [math]\left(5.081,0\right)[/math].[/size][br][br][size=100]What is the name for the points where the graph of a function crosses the [/size][math]x[/math]-axis?
Use a calculator to compute [math]f\left(1.919\right)[/math]. You may use the applet below.[br]
Use a calculator to compute [math]f\left(5.081\right)[/math]. You may use the applet below.[br]
Explain why 1.919 and 5.081 are approximate solutions to the equation [math]0=4x^2-28x+39[/math] and are not exact solutions.[br]
[size=150]Which equation shows a next step in solving [math]9\left(x-1\right)^2=36[/math] that will lead to the correct solutions?[/size]
[size=150]“It started out cool in the morning, but then the temperature increased until noon. It stayed the same for a while, until it suddenly dropped quickly! It got colder than it was in the morning, and after that, it was cold for the rest of the day.”[/size][br]
[size=150]The number of people, [math]p[/math], who watch a weekly TV show is modeled by the equation [math]p=100,000\cdot\left(1.1\right)^w[/math], where [math]w[/math] is the number of weeks since the show first aired.[/size][br][br]How many people watched the show the first time it aired? Explain how you know.
On which week does the show first get an audience of more than 500,000 people?[br]