3.8. 4 Test ( TST ) : Quadratic Equations Date:` Algebra I Sem 2 Points Possible : 50 Answer the following questions using what you've learned from this unit . Write your answers in the space provided . Be sure to show all work . 7 . At the state fair , Erin and her cousin ride the Ultra Drop roller coaster . When the ride plummets. down the first hill , it dips below the loading platform . At the bottom , a camera snaps the riders' picture* before hurtling them back toward the sky . The equation Y = *2 - 9 x + 20 models the roller coaster's path over time . The variable y represents height ( in feet ) above or below the platform . At Y = O , the roller coaster is even with the platform . The variable * represents the amount of time ( in seconds ) since the ride began . Factor and graph the equation to better understand Erin's ride . Part 1 : Write the equation in factored form . ( 1 point ) Part 11 : Find the vertex of the parabola . Hint : To find the *- value of the vertex , take the a the *-values of the x- intercepts or use the first part of the quadratic formula ( * = _ _ ) 7 point for each coordinate value ) 2 . What are the X- intercepts ? Hint : Use the equation from Part 1 . ( 2 points ) Part 111 : Identify the intercepts .b . What is the y-intercept ? Hint : Use the equation Y = x2 - 9 * + 20. ( 7 point ) Part IV : Sketch the graph of Y = *2 - 9 x + 20. Identify the vertex and x- and -intercepts on your* sketch . ( 3 points ) Part V : Use the graph to answer the questions . 2 . Between what times does the roller coaster dip below the platform ? ( 1 point )b . What is the height and time at which Erin's picture is taken during the roller coaster ride ?" Hint : Erin's picture is taken at the lowest point of the roller coaster . ( 1 point ) Completing the Square 2. Solve the equation by completing the square . Show your work . X 2 - 30 * = - 125 Step 1 : Add | {| to both sides of the equation . ( 2 points ) Step 2 : Factor the left side of the equation . Show your work . ( 2 points ) Hint : It is a perfect square trinomial . Step 3 : Take the square root of both sides of the equation from Step 2. ( 7 point )Step 4 : Simplify the radical and solve for x . Show your work . ( 7 point ) 3 . A community is developing plans for a pool and hot tub . The community plans to form a swim team , so the pool must be built to certain dimensions . Answer the questions to identify possible dimensions of the deck around the pool and hot tub * + 3 yds " pris - 2 5 ; its $ 1 25 YO's Part 1 : The dimensions of the pool are to be 25 yards by 9 yards . The deck will be the same width on all sides of the pool . Including the deck , the total pool area has a length of ( * + 25) yards , and a width of ( * + 9 ) yards . 2 . Write an equation representing the total area of the pool and the pool deck . Use y to represent the total area . Hint : The area of a rectangle is length times width . ( 1 point ) 6. Rewrite the area equation in standard form . Hint : Use the FOIL method . ( 7 point )Step 2 : Substitute the area of the enclosed space for Y in your equation . ( 1 point ) Step 3 : Solve your equation from Part b for x . ( 3 points ) Step 4 : What is the width of the deck around the hot tub ? Hint : One of the answers from Part C* is not reasonable . ( 1 point ) Comparing Quadratic Functions 4 . Two different quadratic functions have graphs with the same vertex . Which function's graph increases faster between * = 2 and * = 3 ? Function A Function B V 7.5 0.5 O 2 4 3 0. 5 - 7 5 LO 12.5 - 7 72.5 5a. What is the vertex of each function's graph? (1 point) b. What is the average rate of change in function A between x = 2 and x = 3? (2 points) c. What is the average rate of change in function B between x= 2 and x = 3? (2 points) d. Which function's graph increases faster between x= 2 and x = 3? (1 point) 5. Solve this nonlinear system of equations. Show your work. Solving Systems of Quadratic Equations a Use substitution to combine equations. Rewrite so that one side is equal to 0. (1 point) y = -x2+ 6x - 5 y = 3