[math]x^2=144[/math]

[math]x^2=5[/math]

[math]4x^2=28[/math]

[math]x^2=\frac{25}{4}[/math]

[math]2x^2=22[/math]

[math]7x^2=16[/math]

Is [math]\sqrt{4}[/math] a positive or negative number? Explain your reasoning.[br]

Is [math]\sqrt{5}[/math] a positive or negative number? Explain your reasoning.[br]

Explain the difference between [math]\sqrt{9}[/math] and the solutions to [math]x^2=9[/math].[br]

[size=150]Then, verify that the solutions found using the two methods are close.[/size][br][br][math]x^2+10x+8=0[/math]

[math]x^2-4x-11=0[/math]

[table][tr][td][br][math]\begin{align} p^2-5p&=0\\p(p-5)&=0\\p-5&=0\\p&=5\end{align}[/math][br][/td][td][size=150]She thinks that her solution is correct because substituting [br]5 for [math]p[/math] in the original expression [math]p^2-5p[/math] gives [math]5^2-5\left(5\right)[/math], [br]which is [math]25-25[/math] or 0.[/size][/td][/tr][/table][br]Explain the mistake that Jada made and show the correct solutions.

[size=150]Which expression in factored form is equivalent to [math]30x^2+31x+5[/math]?[/size]

[size=150]Two rocks are launched straight up in the air. The height of Rock A is given by the function [math]f[/math], where [math]f\left(t\right)=4+30t-16t^2[/math]. The height of Rock B is given by [math]g[/math], where [math]g\left(t\right)=5+20t-16t^2[/math]. In both functions, [math]t[/math] is time measured in seconds and height is measured in feet.[/size][br][br]Which rock is launched from a higher point?

Which rock is launched with a greater velocity?

Describe how the graph of [math]f(x)=|x|[/math] has to be shifted to match the given graph.[br][img]data:image/png;base64,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[/img]

Find an equation for the function represented by the graph.