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Chapter 7: Problem 1
In Exercises 1-20, plot the given point in a rectangular coordinate system. \((1,4)\)
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Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y<12\), it's not necessary for me to graph the linear equation \(3 x-4 y=12\) because the inequality contains a \(<\) symbol, in which equality is not included.
Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}4 x-5 y \geq-20 \\ x \geq-3\end{array}\right.\)
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. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \boldsymbol{x}, \text { Ball's } \\ \text { Horizontal } \\ \text { Distance } \\ \text { (feet) } \end{array} & \begin{array}{c} \boldsymbol{y}, \\ \text { Ball's } \\ \text { Height } \\ \text { (feet) } \end{array} \\ \hline 0 & 6 \\ \hline 0.5 & 7.4 \\ \hline 1.5 & 9 \\ \hline 4 & 6 \\ \hline \end{array} $$ $$ \begin{array}{|l|} \hline u a d R e g \\ y=a \times 2+b x+c \\ a=-.8 \\ b=3.2 \\ c=6 \end{array} $$ 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.
Use the directions for Exercises 9-14 to graph each quadratic function. Use the quadratic formula to find \(x\)-intercepts, rounded to the nearest tenth. \(f(x)=-3 x^{2}+6 x-2\)
Graph each linear inequality. \(2 x-5 y<10\)
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