91Ó°ÊÓ

Multiple Choice The period of a pendulum is the time the pendulum takes to swing back and forth. The function \(\ell=0.81 t^{2}\) relates the length \(\ell\) in feet of a pendulum to the time \(t\) in seconds that it takes to swing back and forth. The convention center in Portland, Oregon, has the longest pendulum in the United States. The pendulum's length is 90 ft. Find the period. A 8.5 seconds B 10.5 seconds C 90 seconds D 111 seconds

The graph of each function contains the given point. Find the value of \(c .\) $$ y=x^{2}-c ;(4,8) $$

Open-Ended Write an equation in standard form that you can solve by factoring and an equation that you cannot solve by factoring.

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary. $$ 2 x^{2}+x+28=0 $$

Sports The height of a punted football can be modeled with the quadratic function \(h=-0.01 x^{2}+1.18 x+2 .\) The horizontal distance in feet from the point of impact with the kicker's foot is \(x,\) and \(h\) is the height of the ball in feet. a. Find the vertex of the graph of the function by completing the square. b. What is the maximum height of the punt? c. The nearest defensive player is 5 ft horizontally from the point of impact. How high must the player reach to block the punt? d. Suppose the ball was not blocked but continued on its path. How far down field would the ball go before it hit the ground? e. Critical Thinking The linear equation \(h=1.13 x+2\) could model the path of the football shown in the graph. Why is this not a good model?

Critical Thinking What is the minimum number of data points you need to find a quadratic model for a data set? Explain.

Find the value of \(k\) that would make the left side of each equation a perfect square trinomial. $$x^{2}+k x+25=0$$

A model for the height of an arrow shot into the air is \(h(t)=-16 t^{2}+72 t+5\) where \(t\) is time and \(h\) is height. Without graphing, consider the function's graph. a. What can you learn by finding the graph's intercept with the \(h\) -axis? b. What can you learn by finding the graph's intercept(s) with the \(t\) -axis?

For each function, the vertex of the function's graph is given. Find \(c .\) $$ y=x^{2}-6 x+c ;(3,-4) $$

Solve each equation. Check your answers. $$ -5 x^{2}-3=0 $$