Chapter 3 Review 1 . Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. a. f (x )= -(x-1)2+4 b. f (x ) = - x2 + 2x+ 3 2. Use the equation f (x)=-x +14x-106, not its graph, to find a) the maximum or minimum value and where it occurs, b) the function's domain and range. 3. Among all pairs of numbers whose differences is 14, find a pair whose product is as small as possible. What is the minimum product? 4. Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. a. f (x)=x-6x*+9x2 b . f ( x ) =-x+1 5. The polynomial function f (x)=-0.87 x +0.35 x +81.62 x+7684.94 models the number of thefts, f (x), in thousands in the United States x years after 1987. Will this function be useful in modeling the number of thefts over an extended period of time? Explain. 6. Find the zeros for the polynomial function f (x)=x-5x -25 x+125 and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. 7 . For the following functions, a) use the Leading Coefficient Test to determine the graph's end behavior, b) determine whether the graph has y-axis symmetry, origin symmetry or neither, c) Graph the function. a. f (x) =x-x -9x+9 b. f(x)=2x +3x-8x-12 c. f (x ) =-x +6x-9x 8. Graph the polynomial function f (x)=2x(x-1)'(x+2) 9 . Divide using long division: a. (4x -3x-2x+ 1)=(x+1) b. (4x *+6x +3x-1)=(2x2+1) 10. Divide using synthetic division: (3 x*-2x2-10 x)=(x-2) 11. Divide using synthetic division and then use your result to find all zeros of the function. (2x)+ x-13x+6):(x-2) 12. Use the Rational Zero Theorem to list all the possible rational zeros for f (x)=x- 6x +14x2-14x+5