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Mathematical Investigations III Poly Quiz Sheets 1-8 Name __________________ No Calculator. Show your work to receive full credit: 1 a. Complete the square on the following and give the vertex and zeroes of the parabola. Show your work. Vertex: Roots: 13 y 5 0 2( x 3) 2 13 ( x 3) 2 y 2 x 2 12 x 5 x2 6x 2 2 13 y 5 ( x 3) 9 x2 6 x 9 2 2 y 5 13 9 ( x 3) 2 x 3 2 2 2 y 2( x 3) 13 So Vertex = (3, 13) b. Sketch the parabola y 2 x 2 12 x 5 below. Clearly indicate significant points . Label the scales on both axes. Neatness and accuracy count . 2. Given f ( x) ax 2 bx c . Explain how you can determine if the roots of this quadratic are complex or realm without solving for the roots. We look at b 2 4ac . If this quantity, called the discriminant, is negative the roots are complex IMSA SP 12 3. Write an equation (if possible) for the polynomial function which meets the following criteria: a. cubic, a single root of multiplicity one at x = 5 and no other x-intercepts. y ( x 5)( x 2 1) b. fourth degree with three real roots. y ( x 5)2 ( x 1)( x 3) c. a fifth degree polynomial with a bounce point at x = 3, a pass through point at x 2 , and no other x-intercepts. y ( x 3)2 ( x 2)3 or perhaps y ( x 3)2 ( x 2)( x 2 1) 4. All even degree polynomials are even functions. True or False? Explain. This is false. For example, f ( x) x 2 x has degree 2 which is an even degree, but this function is not even. f ( x) ( x)2 ( x) x 2 x f ( x) 5. Sketch the graph of each polynomial. Label all intercepts. a. 2( x 3)( x 3) 2 b. ( x 1)3 ( x 2)2 (2 x) 6. Label each as a polynomial (p) or not a polynomial (n): a. f ( x) x 3 3 x 2 4 b. g ( x) x x 2 3 c. h( x) 3x3 x 2 3 4 1 d. g ( x) x 3 x 2 x x IMSA SP 12