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.
