Vocabulary
(x+5)+(3x+9)
4x + 14
y = x
Positive infinity as x goes to positive infinity.
Positive infinity as x goes to negative infinity.
Describe the concavity and state the y-intercept:
y= x2+ 2x + 3
Concave up and y-intercept of 3
Name the following for y = 2x4+9x3-5x2+6
Degree, leading coefficient, and constant term.
Leading coefficient = 2
Constant = 6
(3x2+4x)+(2x2-3x)
5x2+x
y = x2
Positive infinity as x goes to positive infinity.
Positive infinity as x goes to negative infinity.
What is this graph's y-intercept?
y= (x + 2) (x + 1)
How many terms are in this polynomial and how many terms could be added without changing the degree?
y = 4x5+6x-3
Three terms.
Three more could be added.
(2x-4)-2(4x-2)
-6x
Describe this graph's end behavior:
y = x4
Positive infinity as x goes to positive infinity.
Positive infinity as x goes to negative infinity.
What are the roots of this equation?
y = x2 + 5x + 6
x = -1 and x = -5
If a polynomial has degree 7, what is the most number of terms it could have? What is the least?
Most is 8, least is 1.
(6x3+4x2-4x+5)-2(2x3-3x2+5x-5)
2x3+10x2-14x+15
Describe this graph's end behavior:
y = x3
Positive infinity as x goes to positive infinity.
Negative infinity as x goes to negative infinity.
y = 2(x -3)2 + 12
(3, 12)
"Like terms" need to have this in common.
Same exponent on the variable.
(5x3+4x2-2x+2)+2(2x3-2x2+x+5)
9x3+12
Describe this graph's end behavior:
y = -x4 + 3x3 + 2x + 6
Negative infinity as x goes to positive infinity.
Negative infinity as x goes to positive infinity.
Mr. Boucher wants to know how many desks can fit in his classroom next year. The length of his classroom is x+5 ft and the width of her classroom is x-4 ft. What is the area of the classroom?
x2+x-20 square ft
Solve the system of equations (use substitution or elimination):
y = 3x - 2
y = -x - 6
(-1, -5)