1) Solve the quadratic equation Y=5x*+3 where *=2 A. x = (Y-3) B. x = (3+Y) C. x = (3+Y) 2 D. x = (Y-3) 2

Transcription

1 TEST 13 REVIEW Quadratics 1) Solve the quadratic equation Y=5x*+3 where *=2 A. x = (Y-3) B. x = (3+Y) C. x = (3+Y) 2 D. x = (Y-3) 2 2) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x+14. 3) Find the domain and range Domain: Range: A)1 B) 2 C) x times itself D) Y times itself 4) Find the Axis of Symmetry on the graph below. A) 1 B) -5 C) -1 D) 3

2 Graph this quadratic equation 2 y = 2x - 16x Solve Quadratic Equation 5x + 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 +12t. What s the maximum height your feet will be above the ground? X Y

3 1. Where are the zeros located on the graph below. 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. I,III,II,IIII C. III,I,II,IIII D. IIII,I,II,III 4. A car is traveling at a constant speed, after 3 hours the car has traveled 180 miles. If the car keeps moving at the same speed, how much more hours will it take for the car to travel 270 miles? A. 1 more hour B. 3 more hours C. 1 ½ more hours D. 2 more hours

4 X Y ? The data in the table shows ordered pair solutions to a linear function. Find the missing y-value. show your work.

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 , where x is the time in seconds. How long did it take for the glasses to reach the ground 2. Find the vertex of the parabola. 3. Is this function quadratic? 4. Graph the quadratic function below. 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 select the zeros of this equation. a. (2 and 2) b. (3 and 0) c. (2 and 4) d.( 2 and -3 ) 3. Find the zeros on the table x y Is this a quadratic function? Explain your reasoning. 4. 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)

7 1. How does a quadratic equation look when graphed? a. it s a straight line c. it s only one fixed point b. like a parabola d. there s two curved lines that never meet 2. (ax 2 + bx + c) is: a. a quadratic formula c. not able to be graphed b. a parabola d. a and b e. always in all four quadrants when graphed 3. In the quadratic formula x = a. always a vertex c. an intercept b. a solution d. a zero 4. Use the factoring method(gcf)to solve for 3x 2 + 6x + 3

8 1. Between what two numbers will the graph of this equation meet the y-axis? y=⅓(x+2) 2 +6 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 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 three. b) Because X increases at a constant rate. c) Because Y increases at a constant rate. d) Because the graph of the equations is a parabola. x y KEY: 1C 2A 3C 4C

9 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. 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 BLANK 4. How many solutions are in the equation y = x 2

10 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 of the polynomial above? A. 4 B.7 C.-2 D.2

11 x Y What is the vertex of the quadratic to the left? A. 11 B. -2 C. 4 D Graph the following equation. Y=5x^2+2 KEY: 1A 2D 3D

12 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.

13 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

14 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 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

15 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= 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) = 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) 3. Y = 2x + 5 X Y (x,y) Solve x^2 + 5x + 6 = 0

16 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

17 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.