A set of college algebra problems on quadratic functions, with answers, are presented. The solutions are at the bottom of the page.
Problem 1Write the quadratic function f(x) = 2x^{2} 12x  20 in standard form (or vertex form).Problem 2Let f(x) =  2 x^{2} + 4x + 6.a) Find the vertex of the graph of f. b) Find the range of f. c) Find the x  intercepts of the graph of f. c) Find the y  intercept of the graph of f. Problem 3f is a quadratic function whose graph has a vertex at the point (3 , 2) and has a yintercept at the point (0 , 16).a) Find the equation for function f. b) Find the xintercepts of the graph of f. Problem 4Find all values of b and c so that the quadratic function f(x) = x^{2} + bx + c has a graph that is tangent to the x axis and a yintercept at (0 , 4).Problem 5Find the equation of a quadratic function f whose graph has a vertical axis of symmetry x = 2, the range of f is given by the interval [4 , +infinity) and f(2) = 8.Problem 6A graph of a parabola is shown below. Finda) The vertex of the parabola. (round the x and y coordinates to the nearest integer). b) The x and y intercepts of the parabola. (round the x and y coordinates to the nearest integer). c) The equation of the axis of symmetry of the parabola. d) The equation of the line tangent to the parabola at the vertex. e) The equation of parabola. Problem 7A rectangular picture measuring 10 cm by 15 cm is surrounded by a frame with uniform width x. Write a quadratic function that gives the area A of the frame as a function of x.Problem 8Function g is given by g(x) = 2(x  3)(x 7). Find the value of x that makes g(x) maximum.
Solutions to the Above ProblemsSolutions to Problem 1f(x) = 2x^{2} 12x  20 = 2(x + 3)^{2}  2 (completing square)Solutions to Problem 2
Solutions to Problem 3
Solutions to Problem 4c = 4 , b = 4 or 4Solutions to Problem 5f(x) = (1/4)(x + 3)^{2} + 4Solutions to Problem 6
Solutions to Problem 7A = (10 + 2x)(15 + 2x)  10*15 = 4x^{2} + 50xSolutions to Problem 8g(x) is maximum at x = 10More References and linksVertex and Intercepts Parabola ProblemsFind Range of Quadratic Functions How to Find x and y Intercepts Of Graphs quadratic functionAlgebra Questions and problems More ACT, SAT and Compass practice
