91Ó°ÊÓ

The vertical line passing through the vertex of a parabola is called the _________.

A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 75 meters above the road surface and are 400 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 100 meters from the center. (Assume that the road is level.

In Problems \(11-16\) (a) Draw a scatter plot. (b) Select two points from the scatter plot, and find an equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter plot. (d) Use a graphing utility to find the line of best fit. (e) What is the correlation coefficient \(r\) ? (f) Use a graphing utility to draw the scatter plot and graph the line of best fit on it. $$ \begin{array}{|l|lllllll|} \hline x & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ y & 4 & 6 & 7 & 10 & 12 & 14 & 16 \\ \hline \end{array} $$

What is the only type of function that has a constant average rate of change? (a) linear function (b) quadratic function (c) step function (d) absolute value function

A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola. Then calculate the height of the arch at points 10 feet, 20 feet, and 40 feet from the center.

(a) Draw a scatter plot. (b) Select two points from the scatter plot, and find an equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter plot. (d) Use a graphing utility to find the line of best fit. (e) What is the correlation coefficient \(r\) ? (f) Use a graphing utility to draw the scatter plot and graph the line of best fit on it. $$ \begin{array}{|l|llllll|} \hline x & 3 & 5 & 7 & 9 & 11 & 13 \\ y & 0 & 2 & 3 & 6 & 9 & 11 \\ \hline \end{array} $$

True or False If the discriminant \(b^{2}-4 a c=0,\) the graph of \(f(x)=a x^{2}+b x+c, a \neq 0,\) touches the \(x\) -axis at its vertex.

A linear function is given. (a) Find the slope and y-intercept of each function. (b) Use the slope and y-intercept to graph each function. (c) What is the average rate of change of each function? (d) Determine whether each function is increasing, decreasing, or constant. $$ g(x)=5 x-4 $$

A linear function is given. (a) Find the slope and y-intercept of each function. (b) Use the slope and y-intercept to graph each function. (c) What is the average rate of change of each function? (d) Determine whether each function is increasing, decreasing, or constant. $$ p(x)=-x+6 $$