For each problem write an equation to represent the situation, then solve the equation using factoring and state the solution.

  1. The length of each of a pair of parallel sides of a square is increased by 2 meters, and the length of each of the other two sides is decreased by 2 meters. The area of the rectangle formed is 32 square meters. Find the measure of one side of the original square.

Equation: ______

Solution: ______

  1. The length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number

Equation: ______

Solution: ______

  1. The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than eight times the age of the oldest child. Find the ages of the three children.

Equation: ______

Solution: ______

  1. The perimeter of a rectangle is 40 meters. The area is 75 meters. Find the length and width.

Equation: ______

Solution: ______

  1. Joe’s rectangular garden is 6 meters long and 4 meters wide. He wishes to double the area of his garden by increasing its length and width by the same amount. Find the number of meters by which each dimension must be increased

Equation: ______

Solution: ______

  1. Jimmy tossed an apple to Amena, who was on a balcony 40 ft above him, with an initial speed of 56 ft/s. Amena missed the apple on it way up, but caught it on its way down. How long was the apple in the air?

Solution: ______

  1. The height of a flare fired from the deck of a ship in distress can be modeled by . Find the time it takes for the flare to hit the water.

Solution: ______

Solve the equation. Express irrational solutions in simplest form (simplify radicals wherever possible). If the equation has no real solution, write “no real solution”.

  1. 8. ______
  1. 9. ______
  1. 10. ______
  1. 11. ______
  1. 12. ______
  1. 13. ______

Name ______Date ______

Algebra Unit E

Quiz 1 Lessons 1 to 4, PART II, Graphing calculator allowed

Use a graphing calculator to answer the questions below. GIVE ALL ANSWERS TO THE NEAREST TENTH.

  1. A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s. The formula for the motion is .
  • At what time will the rocket reach it’s maximum height? ______
  • What is the maximum height? ______
  • How long will it take the rocket to hit the ground? ______
  1. The height, y, in feet of a soccer ball after it is kicked can be modeled by the equation y = -0.04x2 + 1.2x, where x is the horizontal distance in feet that the ball travels. If the ball is kicked so that it reaches its maximum height when it is at the goal and the goal is 8 feet high, assuming the goalie does not block the shot, will the ball go in the goal? How do you know?

______

  1. A ship drops anchor in a harbor. The anchor is 49 feet above the surface of the water when it is released. Use the vertical motion formula: where . How long will it take the anchor to hit the water, assuming the initial velocity is zero.

______

  1. An amateur rocketry club is holding a competition. There is cloud cover at 1000 feet. If a rocket is launched with a velocity of 315 ft/s, use the function to determine how long the rocket is out of sight.

______

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