91Ó°ÊÓ

To prepare for Section \(11.2,\) review evaluating expressions and simplifying radical expressions (Sections \(1.8,10.3\) and \(10.8)\) Evaluate. [ 1.8] $$ b^{2}-4 a c, \text { for } a=1, b=-1, \text { and } c=4 $$

To prepare for Section \(11.2,\) review evaluating expressions and simplifying radical expressions (Sections \(1.8,10.3\) and \(10.8)\) Simplify. \([10.3],[10.8]\) $$ \sqrt{200} $$

To prepare for Section \(11.2,\) review evaluating expressions and simplifying radical expressions (Sections \(1.8,10.3\) and \(10.8)\) Simplify. \([10.3],[10.8]\) $$ \sqrt{-4} $$

To prepare for Section \(11.2,\) review evaluating expressions and simplifying radical expressions (Sections \(1.8,10.3\) and \(10.8)\) Simplify. \([10.3],[10.8]\) $$ \sqrt{-25} $$

Find an equation for a quadratic function \(F\) that satisfies the following conditions. The graph of \(F\) is the same shape as the graph of \(f,\) where \(f(x)=-\frac{1}{3}(x-2)^{2}+7,\) and \(F(x)\) is a maximum at the same point that \(g(x)=2(x+4)^{2}-6\) is a minimum.

If \(f(x)=\left(x-\frac{1}{3}\right)\left(x^{2}+6\right)\) and \(g(x)=\) \(\left(x-\frac{1}{3}\right)\left(x^{2}-\frac{2}{3}\right),\) find all \(a\) for which \((f+g)(a)=0\).

A barge and a fishing boat leave a dock at the same time, traveling at a right angle to each other. The barge travels \(7 \mathrm{km} / \mathrm{h}\) slower than the fishing boat. After 4 hr, the boats are \(68 \mathrm{km}\) apart. Find the speed of each boat. (IMAGE CANNOT COPY)

Find three consecutive integers such that the square of the first plus the product of the other two is 67 .