Quadratics IIPage 1

  1. Find the equation of the parabola that passes through the origin and has a vertex of (4,8)
  1. Find the equation of the parabola with x-intercepts 3 and 6 and y-intercept of –2.
  1. Find the equation of the parabola that passes through the origin and has a vertex of (5,10).
  1. Find the equation of the parabola that passes through the points , , .
  1. Find the values of k that for which has the following x-intercepts: 0 intercepts, 1 intercept, or 2 intercepts.

Not required to do

  1. The parabola passes through the point. Find the equation of this parabola in vertex form.
  1. The parabola passes through the point. Find the equation of this parabola in vertex form.
  1. Find the quadratic function that has an axis of symmetry at , the y-intercept is 1, and there is only one x intercept.
  1. You have a 1200-foot roll of fencing and a large field. You want to make threeenclosures by splitting a rectangular enclosure into three separate areas. What are the dimensions of the largest such enclosure?
  1. Your factory produces lemon-scented widgets. You know that each unit is cheaper, the more you produce, but you also know that costs will eventually go up if you make too many widgets, due to storage requirements. The guy in accounting says that your cost for producing x thousands of units a day can be approximated by the formula. Find the daily production level that will minimize your costs.
  1. You run a canoe-rental business on a small river in Ohio. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day, and vice versa. Use this information to attempt to maximize your income. What should you charge?

Lower your price 50 cents three times. $10.50 per rental.

  1. The owner of a ranch decides to enclose a rectangular region with 140 feet of fencing. To help the fencing cover more land, he plans to use one side of his barn as part of the enclosed region. What is the maximum area the rancher can enclose?

2450 feet

Calculator Problems – please use your calculator to solve the following problems.

  1. A local grocery store has plans to construct a rectangular parking lot on land that is bordered on one side by a highway. There are 1280 feet of fencing available to enclose the other three sides. [Let x represent the length of the two parallel sides of fencing.] Find the dimensions that will maximize the area of the parking lot.
  1. The Mr. C Luggage Company has determined that its profit on its Luxury Ensemble is given by, where x is the number of units sold.

a)What is the profit on 50 units? 100 units?

b)How many units should be sold to maximize profit? In that case, what will be the profit on each unit?

a)50 units, $20,000

100 units $70,000

b)200 units max, $550 profit per unit

  1. During the Civil War, the standard heavy gun for coastal artillery was the 15-inch Rodman cannon, which fired a 330-pound shell. If one of these guns is fired from the top of a 50-foot high shoreline embankment, then the height of the shell above the water (in feet) can be approximated by the function , where x is the horizontal distance (in feet) from the foot of the embankment to a point directly under the shell.. How high does the shell go and how far away does it hit the water?

Max height 841.92 feet

Distance 13,986.52 feet

Quadratics IIMr. John Cendrowski

Lower Moreland HS