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1. A person throws a baseball into the air with an initial vertical velocity of 30 feet per second and then lets the ball hits the ground. The ball is released 5 feet above the ground. For how many seconds is the ball in the air? (Use the formula h(t ) 16t 2 v0t h0 ) ( x y)( x y)( x 2 y 2 ) 2. A city wants to increase the area of a rectangular playground that is 72 feet by 48 feet by adding the same distance x to the length and the width. The new area is to be no more than double the current size. Write and solve an equation to find the maximum value of x. 3 i 15 x 2 3. A football was kicked at the beginning of a game. The “hang time” of the football was 3 seconds, and it reached a height of 36 feet. Write the quadratic equation in factored form that describes the path of the football. y x 2 3x 4 4. Using the discriminant, determine the number and nature of the roots for each of the following quadratic equation. x2 – 8x + 14 = 0 5 1 y 0, y , y 2 3 5. Using the discriminant, determine the number and nature of the roots for each of the following quadratic equation. x2 – 8x + 16 = 0 -6 1 6. Find the missing length A 2 x 13x 15 2 5 y ( x 4) 2 8 4 L x+5 7. Given f(x) = 3x2 + 7x – 6, write f(x) in factored (-5,32) 8. Given the graph of f(x), write the equation of f(x) in: a. Factored form b. Vertex form 90 9. Given the inequality y > x2 + 7x + 12, which point is a solution. a. (-3, 0) b. (0, 12) c. (-2, 3) d. (-1,-1) f ( x) 3( x 5)( x 1) S ( x) 3 x 2 12 x 15 V ( x) 3( x 2) 2 27 10. Given the graph, determine which of the following pairs of zeros could correspond. A. -4.76 and 1.76 B. -5.16 and 1.16 C. -2 and -10 D. -6.42 and 2.42 (1,0) (-3,0) 11. Solve the following equation. 0 = 2x2 + 6x + 12 2x + 3 12. Solve the following inequality. x 5x 6 2 f ( x) ( x 3)(3x 2) 13. Find the vertex of the following parabola: y x2 10 x 7 2 real roots 14. You have an arched window. You are modeling the arch on a coordinate plane. The bottom of the arch is at (-5,0) and (1,0). The arch is 27 units tall. Write the 3 forms of the Quadratic. y ( x 3)( x 1) y ( x 1) 2 4 15. Write the equation of a parabola with a vertex of (-4, -8) and a y-intercept of 12. y 16 x( x 3) 16. Find the roots of a parabola: y 2( x 1)( x 3) c 17. Mr. Jones is making a vegetable garden. The area needed for each watermelon and its surrounding area is 450 square inches. Mr. Jones is planting them in a rectangular garden that the length is 20 inches less than 3 times its width. Mr. Jones planted 50 plants. What is the width? 1 real root 18. Find the area of the triangle whose base is x 4 and whose height is (2 x 2) 2.03 19. Factor: x y 4 B 4 20. Factor and solve: 6 y 13 y 5 y 0 3 2 x 24 KEY! 1>18>3>15>6>11>2>20>4>13 7>12>5>17>8>14>9>16>10>19>1