|
Write the equation for the graph below in standard form, use ^ for power, i.e., the function is in the formy = ax^ 2+bx (no space) If 81 is the discriminant of 2x2 + 5x - k = 0 then the value of k is If one root of the equation x2 + px + 16 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, then the value of q is Given the function f(x) = -3(x +2)2 - 10 a) the function intersect the x- axis at b) the vertext of the function is located at: 0 point write in coordinate format, for example (1,2) 1 point 2 points A soccer ball kicked off the ground has height modeled by the function h = -t2 + 6t, where t is the number of seconds since the ball was kicked and h is the height in meters. What is the maximum height reached by the ball? meters Which of these functions is shown in the graph? B A C D The following diagram shows part of the graph of a quadraticfunction, with equation in the form y = (x - p)(x - q), where p and q are integers and p < q If we rewrite the function in the form y = (x - h)2 + k p = q = k = h = Which functions have negative y - intercepts? ( mark all that applied) y = x2 + 5x - 3 y = 2(x + 3)(x - 2) y = ( x + 2)2 - 1 y = x2 + 4 Which function is the widest? y = -x2 + 3 y =¼ x2 y = ½ x2 + x -1 y = 2x2 + 3 Vertcially stretched by the factor of 2, translate to the left one unit Horizontally stretched by the factor of 2, translate to the left one unit Horizontally stretched by the factor of 2, translate to the right one unit Which series of transformations transform the function f(x) = x2 to the function f(x) = 2( x - 1)2 Vertically stretched by the factor of 2, translate to the right one unit Let f(x) = a(x - h)2 + k, for x ∈ |R The vertext of the graph is at P(3,4) and the graph passes through point Q(1, -4) h = a = k = The solution of x2 - 5x + 6 > 0 is No values of x satisfy this inequality 2 < x < 3 x < 2 or x > 3 1 < x < 6 x < 1 or x > 6 A diver’s path when diving off a platform is given by 𝑑 = −5𝑡2 + 10𝑡 + 20, where 𝑑 is the distance above the water, in feet, and 𝑡 is the time from the beginning of the dive, in seconds. b) After how many seconds is the diver 25 feet above the water? a) How high is the diving platform? sec ft Which graph represents the function y = -x2 + 2x? A B C D Which graph represents the inequality y ≥ x2 - x - 6? A B C D Which inequality is graphed below? y > x2 - 2x - 3 y ≤ -x2 - 2x + 3 y < -x2 - 2x - 3 y ≥ -x2 -2x + 3 Write the quadratic function f(x) = x2 - 8x -17 f(x) = (x - 6)2 -5 f(x) = (x - 6)2 - 9 f(x) = (x - 4)2 - 1 f(x) = (x - 4)2 - 33 The function y = 2(x -1)2 + 5 Its minimum value of y is The axis of symmetry is x = Which order pair is the solution to the given inequalityy < (3x - 1)(x + 2) ? ( mark all that applied) (1,3) (-2,0) (-5,10) (0,5) A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed? Distance = speed Χ time km/h A rock is thrown upward from the top of a 112-foot high cliff overlooking the ocean at a speed of 96 feet per second. The rock’s height above ocean can be modeled by the equation a. When does the rock reach the maximum height? b. What is the maximum height of the rock? H (t) = -16t2 + 96t + 112 t = h = sec ft A B C D The range of the function f(x) = 2x2 + 8x + 5 is y ≥ 5 y ≥ -3 y ≤ 5 y ≤ -3 A travel agent is proposing a tour in which a group will travel in a plane of capacity 150. The fare will be $1400 per person if 120 or fewer people go on the tour; the fare per person for the entire group will be decreased by $10 for each person in excess of 120. For instance, if 125 go, the fare for each will be $1400 - $10×5 = $1350. How many people will give a maximum total revenue? people What is the quadratic function, in vertex form, represented by the parabola below? f(x) = (x - 2)2 +1 f(x) = -(x - 1)2 + 2 f(x) = -(x - 2)2 - 1 f(x) = -(x - 2)2 +1 Angry birds is a popular game in which birds are flung by the use of parabolas. An angry bird's flight is described by the equation ℎ (𝑡) = −5( 𝑡 − 4)( 𝑡 + 2) , where h is the height of the angry bird in meters and at time, t seconds . a) After how many seconds does the bird hit the ground? b) How long does it take for the bird to reach the maximum height? seconds seconds Which function matches the graph? y = x2 - 1 y = x2 + 2x - 1 y = 2x2 - 4x - 1 y = x2 - 2x - 1 What number needs to be added to the following to complete the square? x2 + 8x + n 8 -8 16 32 2 -2 4 -4 2 -2 4 -4 6 -6 Find the zeros of the quadratic function. Then find the axis of symmetry. (1,0) & (0,1) (0, -1) & (-1, 0) (-1, 0) & (1, 0) no zeros axis of symmetry x = 2 -2 4 -4 2 -2 4 -4 6 -6 9.2 Find the zeros of the quadratic function. Then find the axis of symmetry. (1,0) & (2,0) (1, 2) & (2, 2) (0, 0) & (1.5, 0) no zeros axis of symmetry x = |