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.
2.
3.
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
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
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
Poly 6.1
Rev. S11
Mathematical Investigations III
Name:
4.
5.
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
(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 polynomial f (x) having bounce points at x = –3, 1, and 4 and f ( x)  0 for 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 6.2
Rev. S11