Name: _________________________________________________ Quadratics Unit Final Review 1. What are the solutions of the function defined by y = x2 + 9x + 14? 2. What is x2 - 8x + 12in factored form? 3. Rewrite the expression 3x2 – 48 in factored form. 4. Rewrite the expression y2 +5y – 6 in factored form. 5. What is an example of a function that intersects the x-axis at one point? 6. An object is thrown upward out of a building window. The equation h = -16t2 + 40 + 24 models the height in feet, h, of the object above the ground t seconds after it is thrown. How long does it take for the object to hit the ground? 7. What are the solutions to the equation 6x2 + 13x + 6 = 0 8. A toy rocket is launched upward from the ground at a rate of 64 feet per second. The function h(t) = -16t2 + 64 represents h, the height of the rocket, at any given time, t, in seconds after the launch. How many seconds after launch will the rocket hit the ground? 9. What are the values of x in the following equation? (2x – 10)(3x + 12) = 0 10. The height in meters, s, of a rocket t seconds after being launched with an upward velocity of 80 meters per second may be approximated by the equation s = 80t - 5t2. How many seconds after launch is the rocket first 140 meters above the ground? 11. What is the solution set for the equation x2 – 3x = 10? 12. Caleb kicked a ball. The function h(t) = -16t2 + 80t describes the height of the ball, in feet, t seconds after he kicked it. How many seconds did the ball take to first reach 64 feet? 13. What is the minimum value of f(x) = x2 – 10x + 19? 14. The average cost for a company to produce x items is x2 – 10x + 43 dollars. How many items should the company produce to minimize the average cost per item? 15. An outfielder throws a ball vertically upward with a velocity of 30 meters per second. Its distance from the ground after t seconds is approximately equal to 30t – 5t2 meters. How many seconds will it take the ball to reach its maximum distance from the ground? 16. A ball is tossed up into the air from a height of 50 feet. The height, h, of the ball, in feet, is given by the function h(t) = −16t2 + 64t + 50, where t is the time in seconds. What is the maximum height of the ball, in feet? 17. Brad’s scores on three math tests are three consecutive even integers. Write an expression that represents the sum of his test scores. 18. Write an equation to find 3 consecutive integers whose sum is 15. 19. The sum of three consecutive integers is 51. What is the value of the largest integer? 20. For a set of three consecutive odd integers, three times the largest integer is 7 less than twice the sum of the other two integers. What is the largest integer in the set? 21. Five times the width of a rectangle is 9 inches more than 3 times the width. Write an expression for the perimeter of the rectangle. 22. Mary is 21 years old. Her age is 9 years more than 3 times Henry’s age. What is Henry’s age? 23. The perimeter of a rectangular garden is 150 feet. The length is 50 feet longer than the width. What is the width of the garden? 24. The length of a rectangle is 16 inches longer than its width. If the perimeter of the rectangle is 540 inches, what is the length in inches? 25. A rectangle has a length of x and a width of x – 5. What is the perimeter? What is the area?