Polynomials and Rational Functions
Find the vertex of the parabola :
1. x2 + 3x + 3
Graph by hand by finding the vertex, axis of symmetry, x and y intercepts, leading
coefficient , and extra points. Give the domain and range of the function:
2. x2 – 7x + 12
Find the zeros of the function , state the multiplicity, and state if the line crosses or touchs
3. 2x3 – 4x2 + 2x
Prove the function has a zero within the interval by using the Intermediate Value
4. f(x) = x4 – x3 + 3x2 – 5; (0, 2)
Divide using long division:
5. (6x2 + 3x4 – 3x + 2) ÷ (x + 3)
Divide using synthetic division :
6. (7x – 5x5 + 4x2 –8) ÷ (x + 3)
List all possible zeros and find all zeros of the function.
7. x3 – x2 – x – 2 = 0
Find all zeros of the function by using the Rational Zero Theorem, Descartes' Rule of
Signs and quadratic formula .
8. 4y5 + 12y4 – 41y3 – 99y2 + 10y + 24 = 0
Graph the function by finding horizontal, vertical, and/or slant asymptotes, symmetry, x
and y intercepts , and extra points if possible.
Solve the inequality and write answer in interval notation.
a. Find and interpret C(20), C(40), and C(60).
b. Where is the vertical asymptote?
c. Graph the function .