Quadratic Functions
1) Identify the vertex of the graph. Tell whether it is a minimum or maximum.
- (0, 1) maximum
- (0, 0) minimum
- (0, 0) maximum
- (0, 1) minimum
2) Which of the quadratic functions has the narrowest graph?
- y = -3x²
- y = -4x²
- y = 1/7x²
- y = 1/3x
3) If an object is dropped from a height of 39 feet, the function h(t) = −16t² + 39 gives the height of the object after t seconds. Graph the function.
- a
- c
- d
- b
4) A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function h = −16t² + 48t + 8. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
- 1.5 secs, 44 ft
- 1.5 secs, 56 ft
- 1.5 secs, 116 ft
- 3 secs, 8 ft
5) Solve the equation: x² – 15 = 34
- 7
- ±7
- No real number solutions
- ±49
6) Solve (x - 8)(4x + 2) = 0 using the Zero Product Property.
- x = -8, 1/2
- x = -8, -1/2
- x = 8, 1/2
- x = 8, -1/2
7) Solve the equation by factoring: z² − 4z −12 = 0
- z = 6, 2
- z = 6,-2
- z = -6, -2
- z = -6, 2
8) Solve the equation by completing the square: x² +2x - 6 = 0
- -1.65, - 3.65
- 2.24, 2.65
- - 8, 6
- 1.86, - 3.86
9) Use the Quadratic Formula to solve the following equations. 2a² - 46a + 252 = 0
- - 18, 28
- 18, 28
- 9, 14
- - 9, - 14
10) Use the Quadratic Formula to solve the following equations. x² + 6x +18 = 0
- -3 ±√-3
- -3 ± 3.3
- 0 , -6
- No solution
11) A rocket is launched from a top of 56-foot cliff with an initial velocity of 135 ft/s. Substitute the values into the vertical motion formula h = - 16t² +vt + c. Let h = 0. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
- 4.8 s
- 0 = - 16t² + 135t + 56; 4.8 s
- 0 = - 16t² + 56t + 135; 0.4 s
- 0 = - 16t² + 56t + 135; 8.8 s
12) For which discriminant is the graph possible?
- b² - 4ac = 4
- None of these
- b² - 4ac = 0
- b² - 4ac = - 9
13) Find the number of real solutions for the following equations. x² - 12x + 36 = 0
- 2
- None of these
- 0
- 1
14) Find the number of real solutions for the following equations. x² - 5 = 0
- 1
- 0
- 20
- None of these
15) Use the following functions to answer the questions: f(x) = 3x − 2, g(x) = 3x² + 2x− 1, h(x) = 4x + 8 and k(x) = 2x² – x − 9. Find (f/h)when x = 2.
- 4
- 1/4
- 2
- 1
16) Use the following functions to answer the questions : f(x) = 3x - 2, g(x) = 3x² + 2x-1, h(x) = 4x + 8 and k(x) = 2x² - x - 9.17. Find f(x) × h(x).
- 12x² - 16
- 12x² + 32x + 16
- 12x² + 32x - 16
- 12x² + 16x - 16
17) Use the following functions to answer the next set of questions : f(x) = 3x - 2, g(x) = 3x² + 2x -1, h(x) = 4x + 8 and k(x) = 2x² - x - 9. Find g(x) + k(x).
- -5x² - x +10
- 5x² + x -10
- x² + 3x +8
- -x² - 3x - 8
18) Use the following functions to answer the next set of questions : f(x) = 3x − 2, g(x) = 3x² + 2x −1, h(x) = 4x + 8 and k(x) = 2x² – x − 9. Find (g - k)(3)
- 26
- 38
- 24
- 86
19) Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = 4x² + 5x - 1
- x = 5/8, Vertex : (5/8, 59/16)
- x = -5/8, Vertex : (-5/8, -91/16)
- x = -5/8, Vertex : (5/8,-41/16)
- x = 5/8, Vertex : (5/8, 37/8)
20) Suppose you have 56 feet of fencing to enclose a rectangular dog pen. The function A = 28x - x², where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.
- Width = 28ft; Area = 196ft²
- Width = 28ft; Area = 420ft²
- Width = 14ft; Area = 196ft²
- Width = 14ft; Area = 588ft²
21) Solve the equation: x² + 20 = 4
- 24
- No real number solutions
- ± 24
- -4
22) Find the zeros of the function h(x)= x² -15x + 50 by factoring
- x = -10 or -5
- x = -2 or - 25
- x = 2 or 25
- x = 10 or 5
23) Find the vertex of the graph of the quadratic function : y = x² – 3
- (0,3)
- (3,0)
- (-3,0)
- (0,-3)
24) Identify the vertex of the quadratic function : f(x) = (x - 4)² - 5
- (-5,4)
- (0,4)
- (4,-5)
- (-5,0)
25) Find the equation of the quadratic function that has the given vertex and given point on its graph. Vertex: (-4,-4) point: (-3,-5)
- P(x) = -x² – 8x – 20
- P(x) = x² + 8x +4
- P(x) = x² + 8x – 4
- P(x) = -x² + 4x – 4
26) Find the equation of the axis of symmetry of the quadratic function: y = (x + 1)² + 8
- y = -1
- x = -1
- x =1
- y = 0
27) Find the maximum or minimum point of the function f(x) = x² + 14x + 40 and state whether it is a maximum or minimum
- (-7,-9); minimum
- (-9,-7); maximum
- (-9,0); minimum
- (0,-7); maximum
28) Solve the equation 10z² + 3z - 3 = 0
- d
- b
- a
- c
29) Evaluate the discriminant, and predict the type and number of solutions of s² + 3s + 8 = 0
- -23, two different imaginary
- 23, two different irrational
- 23, two different rational
- 0, one rational
30) Write a quadratic equation in the form ax² + bx + c = 0 that has the solutions(roots)5,and -3
- x² - 15x + 2 = 0
- x² + 2x - 15 = 0
- x² - 2x - 15 = 0
- x² - 15x - 2 = 0