MATH 137 Exam 2 Name (8 pts) 2. (m) Determine if x - 5 is a linear factor of / (x) =3x' -13x3-31x +105 Show all work required to obtain answers. Answers without supporting work will get no credit, even (Factor Theorem: x - c is a linear factor of a polynomial f(x ) if and only if f (c ) -0) If they are correct. To answer questions, use material discussed in this class. Material from other sources will not get credit, even If the answers are correct (8 pts) 1. For the polynomial function S(x) " (x+4)' (x-5), determine its intercepts with the axes, and its end behavior. Sketch the graph of this function. (b) Find the quotient of dividing f (x)=3x -13x -31.x +105 by x -5. (a) x-intercepts; (b) y-intercept: (c) End Behavior: A x -> -6,, the values of fx) approach (c) Determine all the zeros of f (x) -3x' -13x2 -31x +105 and as x -> co, the values of f(x) approach (16 pts) 3. (a) Determine the vertex of the graph of f (x)= 2(x-1) -3. Sketch the graph of this parabola, and indicate clearly its y - intercept. -10 -9 -8 -7 6 -6 4 -3 -2 -1 1 2 2456 18 -9 -8 -7 -6 -5 - 1 1 56 (b) Determine the vertex, the x - intercepts, and the y -intercept of the (c) x + 3. + 5 -0 graph of y=-x? -8x-7. Sketch the graph of this parabola. (d) (x-4)(x-1) = 10 18 -9 -8 -7 -6 -5 1 -3 -2 -1 2 3 15 6 (e) x -3x -10 -0 (10 pts) 4. Solve the following quadratic equations. If the solutions are imaginary, write them in the (16 pts) 5. (a) The water temperature in an ocean varies inversely to the water's depth, for depths between form a + bi . 250 ft and 500 ft. The temperature at the depth of 500 fi is 28 F. (a) x -61 +5-0 Find the constant of variation & in the equation of variation T =, and complete the | following table of values for the ocean temperature at several depths of the water. Constant of variation A - (b) x+4-0 Depth d Temperature T 250 n 350 n 400 A 500 n