Math Questions With Answers (13): Quadratic Functions

Math Questions with answers on finding maximum and minimum values, vertex, axis of symmetry, interval of increase and decrease and the range of quadratic functions.

Questions 1:
Find the maximum or minimum value of f(x) = 2x2 + 3x - 5

Questions 2:
Find the range of f(x) = -x2 + 4x - 5

Questions 3:
Find the vertex of the graph of f(x) = 3x2 + 6x - 10

Questions 4:
Find the intervals of increase and decrease of f(x) = 6x2 + x - 2

Questions 5:
Find the axis os symmetry of the graph of f(x) = -2x2 - x - 2

Questions 6:
Find the maximum or minimum value of f(x) = -3x2 + 9x

Questions 7:
Find the range of f(x) = x2 + 5x - 2

Questions 8:
Find the vertex of the graph of f(x) = -x2

Questions 9:
Find the intervals of increase and decrease of f(x) = -0.5x2 + 1.1x - 2.3

Questions 10:
Find the axis of symmetry of the graph of f(x) = -0.5x2 + 1.1x - 2.3

Questions 11:
Find the range of f(x) = -(x - 2)2 + 2x + 4

Questions 12:
Find the vertex of the graph of f(x) = -(x + 4)2 + 4x - 2

Questions 13:
Find the equation of the quadratic function f whose maximum value is -3, its graph has an axis of symmetry given by the equation x = 2 and f(0) = -9.

Questions 14:
Find the equation of the quadratic function f whose graph increases over the interval (- infinity , -2) and decreases over the interval (-2 , + infinity), f(0) = 23 and f(1) = 8.

Questions 15:
Find the equation of the quadratic function f whose minimum value is 2, its graph has an axis of symmetry given by the equation x = -3 and f(2) = 1.

ANSWERS TO ABOVE QUESTIONS
1) f has a minimum value equal to -49/8
2) range: (- infinity , -1]
3) vertex at: (-1 , -13)
4) interval of decrease: (-infinity , -1/12) , interval of increase: (-1/12 , +infinity)
5) The axis is a vertical line given by x = -1/4
6) f(x) has a maximum value equal to 27/4
7) range given by interval: [-33/4 , + infinity)
8) vertex at (0 , 0)
9) f increases over the interval (-infinity , 1.1) and decreases over the interval (1.1 , + infinity)
10) axis of symmetry given by vertical line x = 1.1
11) range given by the interval (-infinity , 9]
12) vertex at (-2 , -14)
13) f(x) = -3/2(x - 2)2 - 3
14) f(x) = -3(x + 2)2 + 35
15) It does not exist since f(2) = 1 is smaller than the minimum value 2.

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