IM Alg1.7.5 Practice: How Many Solutions?

Rewrite each equation so that the expression on one side could be graphed and the x-intercepts of the graph would show the solutions to the equation.
[math]3x^2=81[/math]
[math]\left(x-1\right)\left(x+1\right)-9=5x[/math]
[math]x^2-9x+10=32[/math]
[math]6x(x-8)=29[/math]
[size=150]Here are equations that define quadratic functions [math]f[/math], [math]g[/math], and [math]h[/math].[/size] [br][br][table][tr][td][math]f\left(x\right)=x^2+4[/math][/td][td][math]g\left(x\right)=x\left(x+3\right)[/math][/td][td][math]h\left(x\right)=\left(x-1\right)^2[/math][/td][/tr][/table][br]Sketch a graph, by hand or using technology, that represents each equation.[br]
Determine how many solutions each [math]f\left(x\right)=0[/math], [math]g\left(x\right)=0[/math], and [math]h\left(x\right)=0[/math] has. Explain how you know.[br]
[size=150]Mai is solving the equation [math]\left(x-5\right)^2=0[/math]. She writes that the solutions are [math]x=5[/math] and [math]x=-5[/math]. Han looks at her work and disagrees. He says that only [math]x=5[/math] is a solution.[/size][br][br]Who do you agree with? Explain your reasoning.
[size=150]The graph shows the number of square meters, [math]A[/math], covered by algae in a lake [math]w[/math] weeks after it was first measured.[/size][br][br][size=150][img]data:image/png;base64,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[/img][br][br]In a second lake, the number of square meters, [math]B[/math], covered by algae is defined by the equation [math]B=975\cdot\left(\frac{2}{5}\right)^w[/math], where [math]w[/math] is the number of weeks since it was first measured.[/size][br][br]For which algae population is the area decreasing more rapidly? Explain how you know.
[size=150]If the equation [math]\left(x-4\right)\left(x+6\right)=0[/math] is true, which is also true according to the zero product property?[/size]
[size=150]Solve the equation [math]25=4z^2[/math].[br][/size]
Show that your solution or solutions are correct.
To solve the quadratic equation [math]3\left(x-4\right)^2=27[/math], Andre and Clare wrote the following:[br][br][table][tr][td]Andre[/td][td]Clare[/td][/tr][tr][td][math]\begin {align} 3(x-4)^2 &= 27 \\ (x-4)^2 &= 9 \\ x^2 - 4^2 &= 9 \\ x^2 - 16 &= 9 \\ x^2 &= 25 \\ x = 5 \quad &\text{ or }\quad x = \text- 5\\ \end {align}[/math][/td][td][math]\begin{align} 3(x-4)^2 &= 27\\ (x-4)^2 &= 9\\ x-4 &= 3\\ x &= 7\\ \end{align}[/math][br][/td][/tr][/table][br]Identify the mistake each student made.[br]
Solve the equation and show your reasoning.
Decide if each equation has 0, 1, or 2 solutions and explain how you know.
[math]x^2-144=0[/math]
[math]x^2+144=0[/math]
[math]x\left(x-5\right)=0[/math]
[math]\left(x-8\right)^2=0[/math]
[math]\left(x+3\right)\left(x+7\right)=0[/math]
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Information: IM Alg1.7.5 Practice: How Many Solutions?