MAT 143
Test # 2
Chapter 3 and 4
Name ________________________
1.) Given f(x) = 3x2 + 12x + 5
(a) Showing algebraic work, find the x and y-coordinates of the vertex using either completing
the square or the formula (-b/2a)
(b) Find the axis of symmetry
(c) Is the vertex a maximum or minimum of the function?
2.) (a) Find the quotient and the remainder when x4 – 7x2 + 4x + 2 is divided by x - 3
(b) Is (x – 3) a factor of f(x)? Why?
3.) Determine algebraically and show work (not using graphing calculator) whether or not 3 is a
zero of f(x) = -3x2 + x + 21
4.) Write a polynomial function that has a zero of 1 with multiplicity 2 and a zero of -4 with
multiplicity of 3. (You may leave the answer as a product of linear factors; don’t multiply out).
5.) Write a polynomial of lowest degree with 3 and -2i as two of its zeros and multiply it out.
6.) Use the Intermediate Value Theorem to determine, if possible, whether f(x) = 3x3 – 5x2 – 6 has
a zero between 1 an 3. (Show algebraic work for credit).
7) Use the Rational Zeros Theorem to list (yes, just list) all possible rational zeros of
P(x) = 3x3 + x2 – 11x – 10
8) Find (exactly) all of the zeros of the polynomial P(x) = x3 – 8x2 + 17x - 6
(Show algebraic work for credit).
9) Solve 2 x  3  9 (Show algebraic work for credit).
10) Solve 5x2 + 6x > 8 (Show algebraic work for credit).
11) Solve
x 1
 3 (Show algebraic work for credit).
x2
12) A stone is thrown directly upward from a height of 30 ft with an initial velocity of 60 ft/sec.
The height of the stone t seconds after it has been thrown is given by the function
s(t) = -16t2 + 60t + 30. Determine the time at which the stone reaches its maximum height and find
the maximum height. (You may use your calculator) ----Change your window y-max to 100 ----
13) Sketch a possible 4th degree polynomial that has a leading coefficient is a positive number, a
zero of 0 with multiplicity of 2, a zero of -2 with multiplicity of 1 and a zero of 3 with multiplicity
of 1.
y
y
x
x
Extra credit for test #2
1) Write the formula for the different quotient
2) Write the quadratic formula
3) If f(x) is a polynomial function of degree n, then it has at most _______ real zeros, and at most
_______ turning points
4) Write the formula for the vertex of a parabola
5) Given f(x) = a(x – h)2 + k
The vertex is (
)
Line of symmetry is