1. Use the discriminant to determine the number of x-intercepts of the graph of the equation.

y = x² x + 3

2. Use the discriminant to determine the number of x-intercepts of the graph of the equation.

y = x² 12x + 36

3. Find the coordinates of the x-intercepts of the parabola given by the equation.

a. y = x² 8

b. y = 2x² + x - 3 4.Graph the function.

f(x) = x² 4x 7

5. The bird capable of the fastest flying speed is the swift. A swift flying with the wind to a favorite feeding spot traveled 42 mi in 0.3 h. On returning, now against the wind, the swift was able to travel only 33 mi in the same amount of time. What is the rate of the swift in calm air, and what was the rate of the wind?

6. A whale swimming against an ocean current traveled 120 mi in 3 h. Swimming in the opposite direction, with the current, the whale was able to travel the same distance in 1.5 h. Find the speed of the whale in calm water and the rate of the ocean current.

7. A plane traveling with the wind flew 3625 mi in 6.25 h. Against the wind, the plane required 7.25 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind. 8. Flying with the wind, a plane flew 720 mi in 3 h. Against the wind, the plane required 4 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind

9. A motorboat traveling with the current went 35 mi in 3.5 h. Traveling against the current, the boat went 6 mi in 3 h. Find the rate of the boat in calm water and the rate of the current.

10. A contractor buys 20 yd² of nylon carpet and 28 yd² of wool carpet for $1440. A second purchase, at the same prices includes 15 yd² of nylon carpet and 25 yd² of wool carpet for $1220. Find the cost per square yard of the wool carpet. 11. During one month, a homeowner used 200 units of electricity and 130 units of gas for a total cost of $80.20. The next month, 260 units of electricity and 200 units of gas were used for a total cost of $108.60. Find the cost per unit of gas.

12. A merchant mixed 10 lb of a cinnamon tea with 4 lb of spice tea. The 14-pound mixture cost $18. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $28. Find the cost per pound of the cinnamon tea and of the spice tea.

13. There are various formulas for calculating ideal body weight. In each of the formulas in this exercise, W is ideal body weight in kilograms, and x is height in inches above 60 in. Suppose one researcher gave the following formula for men: W = 53 + 1.9x.

Suppose another researcher published a slightly different formula for men:W = 56.2 + 1.42x.

At what height do both formulas give the same ideal body weight? Round to the nearest whole number.

14. For using a computerized financial news network for 45 min during prime time and 80 min during non-prime time, a customer was charged $11.40. A second customer was charged $13.35 for using the network for 55 min of prime time and 90 min of non-prime time. Find the cost per minute for using the financial news network during prime time.