Mathematical Investigations III
Name:
Mathematical Investigations III- A View of the World
Writing Equations
Write the equation of a polynomial function satisfying each set of given conditions. If the situation is impossible, briefly explain why it is. In many cases, there are an infinite number of possibilities.
1. First degree polynomial which:
(a) crosses the x-axis at x = 3
(b) bounces off the x-axis at x = –2
(c) does not touch the x-axis
2. Quadratic polynomial which:
(a) passes through the x-axis at x = –2 and x = 6
(b) bounces off the x-axis at x = –4
(c) does not touch the x-axis
3. Cubic polynomial which:
(a) crosses the x-axis at x = –1, –4, and 3
(b) bounces off the x-axis at x = 2 and passes through at x = –3
(c) passes through x = 4 with no other zeroes
(d) does not touch the x-axis
4. Quartic polynomial which:
(a) crosses the x - axis at x = –2, 0, 3, and 7
(b) bounces off the x-axis at x = –2 and x = 3
(c) bounces off the x-axis at x = 1 and passes through at x = –3 and 4
(d) passes through x = –1 and x = 5 with no other zeroes
(e) does not touch the x-axis
5. (a) Find a polynomial that has a bounce point at x = 2, a root at x = 0 with multiplicity 3, and passes through at x = –1.
(b) Find a polynomialhaving bounce points at x = –3, 1, and 4 andfor all x.
(c) Find a cubic polynomial that has a root at x = 2 with multiplicity 1 and has no other points of intersection with the x-axis.
(d) Find a polynomial of lowest possible degree that has an x-intercept at 3 with
multiplicity 2, an x-intercept at 5 with multiplicity 3, and an x-intercept at –4 with multiplicity 1.
(e) Find a polynomial with degree 5 having a root at x = –2 with multiplicity 3 and a zero with multiplicity 2 at x = 3 AND whose y-intercept is 48.
Poly 6.XXX Rev. S11