MAT 128 Baltimore City Chapter 3 Transformed Quadratic Equation Worksheet

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Thank you for taking an interest in assisting me with my chapter review assignment. For this assignment I need accurate answers , promptly! I need for all solution to be worked out thoroughly. I need the work to be neat, clear, and detailed step by step to ensure comprehension of solution plus steps. Please SHOW ALL WORK THOROUGHLY!!! Thank you once again for sharing your knowledge.

BCCC
MAT 128
Summer 2020
Professor: Ray Orocco-John
Student’s Name: ________________________________________________
Test #3
Show all work. Answers without adequate justification will not receive full credit. Solve problems
algebraically whenever possible. Simplify to the lowest terms. Underline all final answers.
1. (10 pts) Given P( x) = 2( x − 1)( x + 1)2 ( x + 2) answer the following (you do not have to multiply this out)
a) What is the leading term of P(x)? _____________
b) What is the degree of P(x)?
_____________
c) As x →  the function P ( x ) → _______________
d) As x → − the function P ( x ) → _______________
e) How many turning points (bumps) does it have? ______________
f) Write the coordinates of the x-intercept(s) _____________________________
(indicate if they are single/ double / triple, zeros. i.e. state the Multiplicity of each zero)
g) Find the coordinates of the P-intercept(s) ______________________________
show work algebraically
2. (12pts) Q( x) = −3( x + 1)2 + 4 is a transformed quadratic equation.
a) Sketch the function
b) As x →  the function Q ( x ) → _______________
c) As x → − the function Q ( x ) → _______________
d) What are the coordinates of the Q intercept(s)
e) What are the coordinates of the vertex
f) Is the Vertex a maximum or a minimum?
(g) What are the coordinates of the x intercept(s)
3. (9 pts) A resident of planet Zeldok kicks a ball from
the top of building, and its height after t seconds is
given by h(t ) = −3t 2 + 18t + 9
height
a) What was the height of the building?
b) What is the maximum height the ball reaches?
time
c) When does the ball hit the ground?
4. (6 pts) Given the graph below write the equation for
(show work to find the value of the constant, a)
G(x) = ________________________
G(x)
x
5. (8 pts) Find an equation for a polynomial that would pass through the following points, with long run
behavior f(x) = -x4.
x
f(x)
-2
0
1
3
0
3
0
0
(hint: start by sketching a graph – there is more than one possible answer)
f(x) = ________________________
6. (7 pts) Given the graph below, what is the equation?
H(x) = ________________________
(show work to find the value of the constant, a)
H(x)
x
7. (4 pts) Where is the horizontal asymptote (if any) of m( x) =
b. Explain your answer.
3( x + 3)( x − 2)
( x + 4)2 ( x − 1)
8. (4 pts) Where is the horizontal asymptote (if any) of n( x) =
x2 − 6
5 x − 3x 2
b. Explain your answer.
9. (13 pts) Given: j(x) = (x – 3)
(x2 – 9)
a) What are the coordinates of the x-intercept(s) (if any)? ________________________
b) What are the coordinates of the j-intercepts(s)? _________________________________
c) Where are the vertical asymptotes (if any)? ____________________________________
d) Where are the horizontal asymptotes (if any)? __________________________________
e) As x →  , j ( x) → _______________
f) As x → − , j ( x) → _______________
g) Graph the function and its important
features on the graph paper.
h) The coordinates of a hole in this function
occurs at ( , )
10. (3 pts) Given g ( x)= −3( x − 1)2 + 5 on the restricted domain x  1, find the inverse of g(x)
11. (3 pts) Given k ( x) =
4x
, find k −1 ( x)
5 − 3x
12. (5 pts) Find b and c so that y = −1×2 + bx + c has vertex (6, −2).
13. (4 pts) Find the quotient and remainder using long division:
x4 − 16 ÷ x – 2
14. (6 pts) Find all zeros of the function f(x) = 9×3 − 18×2 − 16x + 32
15. (6 pts) Find all zeros of the function k(x) = x3 – 13x + 12