1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x

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1 TEST 13 REVIEW Quadratics 1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x ) Find the domain and range if the points in the table are discrete Domain: Range: Which best describes the relationship in the table A)1 B) 2 C) x times itself D) Y times itself 3) Find the Axis of Symmetry on the graph below. A) 1 B) -5 C) -1 D) 3

2 Graph this quadratic equation y = 2x 2-16x Solve Quadratic Equation 5x 2 + 9x = Fill in this table y = ½ ( x 4 ) Solve Quadratic Problem You are trying to dunk a basketball. You need to jump 2.5 ft. in the air to dunk the ball. The height that your feet are above the ground in given by the function h(t) = -16t 2 +12t. What s the maximum height your feet will be above the X Y

3 1. Approximate the zeros located on the graph. A. (2,0) (-2,0) B. (0,2) (0,-2) C. (2,0) (0,-2) D. (-3,0) (2,0) 2. What type of graph would the table below represent? X Y A. Quadratic B. Linear C. None of the above 3. I. X 2 II. 3X 2 III. 1/2X 2 IIII. 4X 2 List these equations from narrowest to widest. A. III,I,II,IIII B. IIII,II,I,III C. I,III,II,IIII D. IIII,I,II,III

4

5 1. While on vacation in Italy, Rudy visited the Leaning Tower of Pisa. When he leaned over the railing to look down from the tower, his sunglasses fell off. The height in meters of the sunglasses as they fell can be approximated by the function y= -5x 2 +50, where x is the time in seconds. How long did it take for the glasses to reach the ground 2. Label the vertex, roots, and the axis of symmetry of the parabola. Then find the domain & range. 3. Is this function quadratic? Explain why or why not. 4. If the coefficient of x 2 in the quadratic function below is multiplied by -1/2, how will the graph change? Y=4x 2 5. How does the quadratic function below compare to the quadratic parent function (in terms of the vertex, width, and opening up or down)? Y=4x 2 6. Write an equation that would shift up the vertex of the function Y=4x 2.

6 1. Mathew is working on an equation f(x)=-x 2-4 if he translated by 3 units down which is the most reasonable answer a. Y = -x 2-1 b. Y = 1/3x 2-4 c. Y = -4x 2-4 d. Y = x Graph the following equation: f(x) = 2x 2-6 and approximate the zeros of this equation. a. (2 and 2) b. (3 and 0) c. (2 and 4) d.( 2 and -3 ) 3. Which term best fits the equation 2x 2 -x-15 a. (x-4)(2x+5) b. (x+3)(2x + 5) c.(x-3)(2x + 5) 1. What does the graph of a quadratic equation look like? a. a straight line c. one fixed point b. a parabola d. two curved lines that never meet 2. (ax 2 + bx + c) is: a. the quadratic formula c. not able to be graphed b. a parabola d. the general form of a quadratic equation e. always in all four quadrants when graphed 3. In the quadratic formula the value of x is a. always a vertex c. an intercept b. a solution d. a zero 4. Use the factoring method(gcf) to find the factors for 3x 2 + 6x + 3

7 1. The y-intercept of the equation y=⅓(x+2) 2 +6 is a) Between 5 and 6 b) Between 6 and 7 c) Between 7 and 8 d) Between 8 and 9 2. Which of the following has no real solutions? a) x 2 -x+1=0 b)x 2 -x-1=0 c)x 2 -x-2=0 d)x 2 -x-3=0 3. James kicked a field goal, and wants to figure out how high the ball went in the air. If the path of the football can be represented by -x 2 -x+35, how high did he kick the ball? a) 4 ft b) 10 ft c) 35 ft d) 20 ft 4. Why is this not a quadratic relationship? a) Because the value at zero is one. b) Because X increases at a constant rate. c) Because the ratio of y/x is constant. d) Because the graph of the equations is a parabola. x y KEY: 1C 2A 3C 4C

8 1. Drae, Ethan, and Matthew went to summer camp and rented a canoe. The cost of renting a canoe is modeled by Y = X When Y represents the total cost, X represents the number of hourss rented, and 3 is the one-time cost of entering the store. What is the cost of renting the canoe for three hours? A. $105 C. 3%of entrance fee B. $12 D. $9 2. Write the equation for the graph. What is the solution for Y = 0? 3. Which graph models the equation Y = X ? A. B. Y X B. D. Y X Y X Y X How many solutions are in the equation y = x(x+8)

9 The height of a diver above the water during a dive can be modeled by h=-16t 2 +8t+48, where h is height in feet and t is time in seconds. Find the time it takes for the diver to reach the water. A. t= 3/2x B. t=2/3x C. t= 5/4x D. t= 4/5 What is the line of symmetry in the graph to the right? A. 4 B.7 C.-2 D.2 What is the vertex of the quadratic relationship shown in the table? A. 11 B. -2 C. 4 D. 2 x Y KEY: 1A 2D 3D 2 11

10 1. What is the parent function of the equation y=4x 2-6x+7? a. y=-x b. y=x 2 c. y=x 2 +7 d. y=x+7 2. The area of a new playground is 4x 2 +4x. Find the dimensions (length and width) by factoring. Explain how you got your answer. MUST SHOW ALL WORK! Length: Width: 3. Use the tables below and decide which is a quadratic function. a. c. b.

11 4. (x+2) (x+1) If that is the factoring of a quadratic equation, then which graph matches the factor? a. c. b. Assessment Key 1. B 2. length: 4x width: x+1 3. C 4. A 1.The Area of a rectangle is 4x^2-9. What is the perimeter? A.8x C.4x B.8x+12 D.4x+6 2.A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement? A.12 by 15 B.12 by 16 C.-12 by 16 D.13 by 15

12 3.Which equation represents the quadratic that is graphed below? A.y=x(x-2) C.y=-x(x-2) B.y=x(x-2) D.y=-x(x+2) 4.Complete the table for the graph above and find the axis of symmetry Solve. 1) (x+1) (x-3)=0. Answer: X=-1, 3 2) x^2 + x -4 =0. Answer: X= -1+- square root 17 divided by two 3) x^2-3x -4=0. Answer: X=-1, 4 4) x^2-4=0 Answer: X=+-2

13 1. A ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft. / s. Use the formula h(t) = -16t 2 + vt + s to find how long it will take for the ball to hit the ground. 2. Graph the following quadratic equation y = 3x^2 + x + 1 What is the y - intercept? A. (0,-1) B. (-1,0) C. (-.5,0) D. (.5,0) 1. What are the solutions to X 2 +8X =-15 a) a). x=3 and x=5 b) b). x=-15 and x=-3 c) c). x=-3 and x=-5 d) d). x=9 and x=-5 2. Which equation matches the table? a) A). 4x 2 +8x+1 b) B).5x 2 +8x+7 c) C).8x 2 +4x+1 d) D).9x 2 +7x+2 x y

14 3. What are the zeros of this parabola? a) A). -6 and 1 b) B). 8 and -5 c) C). -8 and 1 d) D). 4 and 9 4. The height of a diver above the water during a dive can be modeled by H = -16t 2 + 8t + 48, where H is height in feet and t is time in seconds. Find the time it takes for the diver to reach the water. Write your answer in a complete sentence. Question 1: C Question 2: A Question 3: C Question 4: Its takes the diver 2 seconds.

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