[center][math]\displaystyle \begin {align} (x+3)^2+9 &=0\\ (x+3)^2 &=\text-9\\ x+3 &=\pm \sqrt{\text-9} \end {align}[/math][/center]Study the example. At what point did you realize the equation had no solutions?
Explain how you know the equation [math]49+x^2=0[/math] has no solutions.[br]
[size=150]The equation [math]h\left(t\right)=-16t^2+80t+64[/math] represented the height, in feet, of a potato [math]t[/math] seconds after it has been launched.[/size][br][br][size=100]Write an equation that can be solved to find when the potato hits the ground. Then solve the equation.[br][/size]
Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation.[br]
[size=150]The equation [math]g\left(t\right)=2+23.7t-4.9t^2[/math] models the height, in meters, of a pumpkin [math]t[/math] seconds after it has been launched from a catapult.[/size][br][br]I[size=100]s the pumpkin still in the air 8 seconds later? Explain or show how you know.[/size][br]
At what value of [math]t[/math] does the pumpkin hit the ground? Show your reasoning.[br]
[size=150]One equation we wrote was [math]\left(7+2x\right)\left(4+2x\right)=38[/math].[/size]
Explain or show what the equation [math]\left(7+2x\right)\left(4+2x\right)=38[/math] tells us about the situation and what it would mean to solve it. Use the diagram, as needed.
Solve the equation without graphing. Show your reasoning.[br]
[size=150]Suppose you have another picture that is 10 inches by 5 inches, and are now using a fancy paper that is 8.5 inches by 4 inches to frame the picture. Again, the frame is to be uniform in thickness all the way [br]around. No fancy framing paper is to be wasted![/size][br][br]Find out how thick the frame should be.
[size=150]Suppose that your border paper is 6 inches by 8 inches. You want to use all the paper to make a half-inch border around some rectangular picture.[br][/size][br]Find two possible pairs of length and width of a rectangular picture that could be framed with a half-inch border and no leftover materials. [br]
What must be true about the length and width of any rectangular picture that can be framed this way? Explain how you know.[br]