91Ó°ÊÓ

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -3 \\ \hline 1 & -2 \\ \hline 2 & 0 \\ \hline 3 & 4 \\ \hline 4 & 12 \\ \hline \end{array} $$

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|r|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & 4 \\ \hline 1 & 5 \\ \hline 2 & 7 \\ \hline 3 & 11 \\ \hline 4 & 19 \\ \hline \end{array} $$

Graph each linear inequality. \(x>0\)

In Exercises 25-36, solve each system by the addition method. Be sure to check all proposed solutions. \(\left\\{\begin{array}{l}x+y=1 \\ x-y=3\end{array}\right.\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}2 x+y<4 \\ x-y>4\end{array}\right.\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}2 x-y<3 \\ x+y<6\end{array}\right.\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}y<-2 x+4 \\ y

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x+2 y \leq 4 \\ y \geq x-3\end{array}\right.\)

A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from where it was thrown. The graphing calculator screen displays a quadratic function that models the ball's height, \(y\), in feet, in terms of its horizontal distance, \(x\), in feet. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { x, Ball's } \\ \text { Horizontal } \\ \text { Distance } \\ \text { (feet) } \end{array} & \begin{array}{c} \boldsymbol{y} \text {, Ball's } \\ \text { Height } \\ \text { (feet) } \end{array} \\ \hline 0 & 6 \\ \hline 1 & 7.6 \\ \hline 3 & 6 \\ \hline 4 & 2.8 \\ \hline \end{array} $$ QuadReg $$ \begin{aligned} &y=a x^{2}+b x+c \\ &a=-.8 \\ &b=2.4 \\ &c=6 \end{aligned} $$ a. Explain why a quadratic function was used to model the data. Why is the value of \(a\) negative? b. Use the graphing calculator screen to express the model in function notation. c. Use the model from part (b) to determine the \(x\)-coordinate of the quadratic function's vertex. Then complete this statement: The maximum height of the ball occurs feet from where it was thrown and the maximum height is feet.

Write each sentence as an inequality in two variables. Then graph the inequality. The \(y\)-variable is at least 2 more than the product of \(-3\) and the \(x\)-variable.