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.

## Question 1Find the maximum or minimum value of f(x) = 2x^{2} + 3x - 5
## Question 2Find the range of f(x) = -x^{2} + 4x - 5
## Question 3Find the vertex of the graph of f(x) = 3x^{2} + 6x - 10
## Question 4Find the intervals of increase and decrease of f(x) = 6x^{2} + x - 2
## Question 5Find the axis os symmetry of the graph of f(x) = -2x^{2} - x - 2
## Question 6Find the maximum or minimum value of f(x) = -3x^{2} + 9x
## Question 7Find the range of f(x) = x^{2} + 5x - 2
## Question 8Find the vertex of the graph of f(x) = -x^{2}
## Question 9Find the intervals of increase and decrease of f(x) = -0.5x^{2} + 1.1x - 2.3
## Question 10Find the axis of symmetry of the graph of f(x) = -0.5x^{2} + 1.1x - 2.3
## Question 11Find the range of f(x) = -(x - 2)^{2} + 2x + 4
## Question 12Find the vertex of the graph of f(x) = -(x + 4)^{2} + 4x - 2
## Question 13Find 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.
## Question 14Find 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.
## Question 15Find 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 QUESTIONS1) f has a minimum value equal to -49/82) 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. ## More References and Linksquadratic functionsGraphing Quadratic Functions math questions and problems with detailed solutions in this site. |