Exam 4: Lines parabolas and Systems

By sketching the graphs (using a graphing calculator or graphing paper)solve the system of

An equation of the straight line passing through (1,-5)and (-2,4)is

The number of solutions of the system is

Suppose the supply and demand equations for a manufacturer's product are and respectively,where q represents number of units and p represents price per unit in dollars.Determine (a)the equilibrium quantity; (b)the equilibrium price.If a tax of $1.00 per unit is imposed on the manufacturer,(c)determine the new equilibrium quantity; (d)the new equilibrium price.

Determine whether the following lines are parallel,perpendicular or neither. 0.1x - 7y + 81 = 0 2x - 140y + 9 = 0

For the parabola y = f(x)= 2 - 4x - 6,find: (a)the vertex,(b)the y-intercept,and (c)the x-intercepts.

State whether the following function has a maximum value or minimum value and find it: f(x)= 2 + 10x -

A manufacturer sells his product at $23 per unit,selling all he produces.His fixed cost is $18,000 and his variable cost per unit is $18.50.The level of production at which the manufacturer breaks even is

Determine a linear function f(x),given f(2)= 0.5; f(1)= -1.

In 1986 the stock in a biotechnology company traded for $30 per share.In 1996 the company started having trouble,and the stock price dropped to $10 per share.Use a graphing calculator to show the relationship between price per share and the year in which it traded.Find and interpret the slope.

Graph the function y = f(x)= - 6x and indicate the coordinates of the vertex and intercepts.

Find the x-intercept made by the line that passes through the points (1,-1)and (-1,0).

A function describing the value of a house purchased for $180,000 after x years of appreciation is estimated to be f(x)= 12,000x + 180,000.Graph the function on your graphing calculator.

Suppose f(1)= -5 and f(-2)= 4.Find f(x)if f is a linear function.

When the temperature T (in degrees Celsius)of a certain laboratory animal is reduced,its heart rate r (in beats per minute)decreases.At a temperature of 37°C,the animal had a heart rate of 200,and at a temperature of its heart rate was 140.If r is a linear function of T for 26 ≤ T ≤ 38,(a)determine this function and (b)determine the heart rate at a temperature of 30°C.

Suppose that consumers will demand 100 units of a product when the price is $10 per unit,and 120 units when the price is $8 per unit.Assuming that price p and quantity q are linearly related,find the price at which 90 units are demanded.

Find the slope of the linear function f(t)= .

For the parabola y = f(x)= - + 7x - 6,find: (a)the vertex,(b)the y-intercept,and (c)the x-intercepts.

A baby weighs 9 pounds at birth and 30 pounds at age 3.Use a graphing calculator to graph the resulting equation and determine how much the child will weight at age 12.

Solve the following system algebraically: