MATH 110 M9 COMPREHENSIVE EXAM
STUDY GUIDE WITH COMPLETE
SOLUTIONS
●● Discriminants
Answer: √b^2-4ac
Tells you how many roots there will be
●● Types of roots- 0, 1, 2
Answer: 0 if it's a -
1 if it's 0
2 if it's a +
●● Horizontal intercepts/roots
Answer: Solve quadratic formula for +/-
●● Concave Direction
Answer: Up if it's a +#
Down if it's a -#
●● i
, Answer: √-1
●● i^2
Answer: -1
●● Add imaginary #'s
Answer: 4i-2i= 2i
●● Multiply imaginary #'s
Answer: 2x5i= 10i
3ix5i= 15i^2 (15x-1)--> -15
●● Change inside the parenthesis
Answer: Affects the x-axis
●● Change outside the parenthesis
Answer: Affects the y-axis
●● f(x)-1
Answer: Shift down 1
●● f(x)+1
STUDY GUIDE WITH COMPLETE
SOLUTIONS
●● Discriminants
Answer: √b^2-4ac
Tells you how many roots there will be
●● Types of roots- 0, 1, 2
Answer: 0 if it's a -
1 if it's 0
2 if it's a +
●● Horizontal intercepts/roots
Answer: Solve quadratic formula for +/-
●● Concave Direction
Answer: Up if it's a +#
Down if it's a -#
●● i
, Answer: √-1
●● i^2
Answer: -1
●● Add imaginary #'s
Answer: 4i-2i= 2i
●● Multiply imaginary #'s
Answer: 2x5i= 10i
3ix5i= 15i^2 (15x-1)--> -15
●● Change inside the parenthesis
Answer: Affects the x-axis
●● Change outside the parenthesis
Answer: Affects the y-axis
●● f(x)-1
Answer: Shift down 1
●● f(x)+1
