1. Is \(\sqrt{4}\) a positive or negative number? Explain your reasoning.
2. Is \(\sqrt{5}\) a positive or negative number? Explain your reasoning.
3. Explain the difference between \(\sqrt{9}\) and the solutions to \(x^2 = 9\).

Technology required. For each equation, find the exact solutions by completing the square and the approximate solutions by graphing. Then, verify that the solutions found using the two methods are close.

Which expression in factored form is equivalent to \(30x^2 +31x+5\)?

Two rocks are launched straight up in the air. The height of Rock A is given by the function \(f\), where \(f(t) = 4 + 30t - 16t^2\). The height of Rock B is given by \(g\), where \(g(t) = 5 +20t - 16t^2\). In both functions, \(t\) is time measured in seconds after the rocks are launched, and height is measured in feet above the ground.

1. Which rock is launched from a higher point?
2. Which rock is launched with a greater velocity?

1. Describe how the graph of \(f(x) = |x|\) has to be shifted to match the given graph.

   

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2. Find an equation for the function represented by the graph.