91Ó°ÊÓ

Explain how to determine the solution set for the inequality \(a x^{2}+b x+c<0,\) where \(a>0 .\) How would the solution set change if \(a<0 ?\)

Solve. Write answers in standard form. $$ 3 x^{2}+x-x(5-x)-2 $$

Solve for the specified variable. $$ V=\frac{1}{3} \pi r^{2} h \text { for } r $$

For the given representation of a function \(f,\) graph the reflection across the \(x\)-axis and graph the reflection across the \(y\)-axis. Line graph determined by the table \(\begin{array}{rrrrr}x & -3 & -1 & 1 & 2 \\ f(x) & 2 & 3 & -1 & -2\end{array}\)

Solve. Write answers in standard form. $$ 3 x(3-x)-8=x(x-2) $$

For the given representation of a function \(f,\) graph the reflection across the \(x\)-axis and graph the reflection across the \(y\)-axis. Line graph determined by the table \(\begin{array}{rrrrr}x & -4 & -2 & 0 & 1 \\ f(x) & -1 & -4 & -2 & -2\end{array}\)

Solve. Write answers in standard form. $$ -x(7-2 x)=-6-(3-x) $$

Solve for the specified variable. $$ V=\frac{1}{2} g t^{2}+h \text { for } t $$

Two functions, \(f\) and \(g,\) are related by the given equation. Use the numerical representation of \(f\) to make a numerical representation of \(\mathbf{g}\). \(g(x)=f(x)+7\) $$\begin{array}{rrrrrrr}x & 1 & 2 & 3 & 4 & 5 & 6 \\\\\hline f(x) & 5 & 1 & 6 & 2 & 7 & 9\end{array}$$

Solve for the specified variable. $$ \boldsymbol{K}=\frac{1}{2} m \boldsymbol{v}^{2} \text { for } \boldsymbol{v} $$