West Valley College Calculus Worksheet

Precalc (Allen)Exam 2 part 1
name
Spring 2022
Please use either dark pencil or pen. To receive credit you must show your work. This exam is worth
150 points.
1) (6 pts) Find the vertex of f(x) = -8×2 + 16x + 24 by completing the square. After that, also identify
the x and y intercepts. Show all of your work.
2) Given polynomial p(x) = 4x – 18×2 – 9×5 + 12, identify the following (8 pts):
a) the lead term is
c) y 
b) the degree of the polynomial is
as x  
d) y 
as x   
3) Given polynomial p(x) = -2(x – (3 + 4i))(x – (3 – 4i))(2x + 1) 3(x + 6)2, answer the following (8 pts):
a) the degree of p(x) is
c) the graph of p(x) touches the x-axis at x =
b) the lead term is
and crosses at x =
.
4) (3 pts) Write a 3rd degree polynomial with integer coefficients with zeros at x = -1/3, 9/7 and 6.
You can leave your answer in factored form.
5) (5 pts) Write the 4th degree polynomial that crosses the x-axis at x = -2 and 3, touches the x-axis at
x = 6, and passes through the point (8, 100)
6) (3 pts) Create a rational function with a horizontal asymptote at y = 0 and vertical asymptotes at
x = -1, and x = 5.
7) (3 pts) Create an example of a rational function with a horizontal asymptote at y = 5, vertical
asymptote at x = -6, and its only x-intercept is at (4, 0)