1. Write the following functions in f(x) = a(x - h)2 + k form. You may use completing the square or the vertex formula h = ->, k = f(h). Then, identify the vertex, the axis of symmetry, the direction of opening, and the range. a) f(x) = 3x2 - 2x + 1 bly = 2x2 - 4x - 1 c) f(2) = x2 - 6x dy = 8 - x2 2. Find all the real and imaginary zeros for the following polynomial functions. a) f(x) = 3x - 1 b ) f ( ac ) = 2 2 - 8 c) f(ac) = 2x3 - 4x2 + 3x d) n(x) = 8x3 + 1 3. Use the rational zeros theorem to list all possible rational zeros for each polynomial function. a) f(x) = -323 +6x2 + 5x-2 b) p(x) = 4x3 - 5x2 - 13x - 8 c) f(x) = 624 - 202 - 92 + 3 d) g(x) = 2x4 + 9x2 - 8x - 3 8 4. Use synthetic division and the remainder theorem to find the indicated value, then check by evaluating for the given value. a) P(x) = 4x3 - 3x2 + x - 1, P(3) b) P(ac) - -825 + 2x3 - 6x + 2, P (-2) 5. Find a polynomial equation of lowest degree with integral coefficients that has the given roots. a ) - 5 , 3 b) 4 + 2i c) 2, 1 - 22 d) -3, 3, -42 6. Use Descarte's rule of signs to discuss the possibilities for the roots to each of the following equations. a) t4 - 3+3 + 2t2 - 5t + 7=0 b) 4x3 - 3x2 + 2x - 9 =0 c) -24 - 23 +3x2 +5x-8=0 d) -5r+ + 4r3 +7r -16-0