Polynomial Functions
f(x)=(x+10)(x+7)(x-12)
What is the degree of the function? Is it odd or even?
3 (odd)
y=abx+k
f(x)=x3-2x2-5x+10
Given x=2 is one of the roots, identify the other two roots
x=10
x=-10
y=(x-2)2-4
Given the function, what is the number of real roots and the number of complex roots?
Real Roots: 2
Complex Roots: 0
Total number of roots: 2
f(x)=(x-3)2(x+3)(x-5)2(x+8)
Find the roots of the function
(-3,0)
(3,0)
(5,0)
y=0.2x(x-m)(2x+4)3
Given the function, identify the Degree and how it impacts the graph
Degree: 5 (odd)
The sides of the graph will open up in opposite directions
Given the intercepts, create an exponential equation:
(1,16) (4,772)
f(x)=x3+3x2-7x-21
Given x=-3 is one of the roots, identify the other two roots
x= 2.645
x=-2.645
y=(x-2)2
Given the function, what is the number of real roots and the number of complex roots?
Real Roots: 1
Complex Roots: 1
Total number of Roots: 2
A Graph of function f(x) has zeros at 3, -3 and 7
Write the Equation
f(x)=(x+3)(x-7)(x-3)
f(x)=(x-2)(x-5)2(x+3)3(x+4)2(x+6)
Given the equation, how many bends, bounces, and crosses does the graph have?
The graph crosses the x-intercept twice, has two bounces, and one bend
A car was originally purchased in January 2000 for $15,000. The car depreciates at a rate of 12% every year. What year will the car be worth half its original value?
y=15,000(1-.12)x
7500=15,000(1-.12)x
.5=(.88)x
log.88(.5)=x
x=5.4 years
In the year 2005
f(x)=x3+3x2-5x-4
Given x=-4 is one of the roots, identify the other two roots
(-0.618,0)
(1.618,0)
y=(x-2)2+3
Given the function, what is the number of real roots and the number of complex roots?
Real Roots: 0
Complex Roots: 2
Total Number of Roots: 2
f(x)=(x+k)(x-p)2
What are the x-intercepts of the function above?
(-k,0)
(p,0)
Write a polynomial equation for a Graph that passes through the point (1,-6) and has three x-intercepts at (-5,0), (-3,0) and (2,0)
Write the equation of an exponential function of the form y=abx+k that passes through the points (-4,239) and (2,-1) and has an asymptote of y=-2
y=6.22(.4008)x-2
Given x=1 is one of the roots, identify the other two roots
(-1.24,0)
(7.24,0)
x2+x-6=0
Given the function, what is the number of real roots and the number of complex roots?
Complex Roots: 0
Total number of roots: 2
f(x)=x2-5x
Find the roots of the function
x=0
x=5
Given the polynomial function equation: f(x)=0.2x(x+7)(5x+8)(x-3)
Identify the key features
x-intercepts: (-7,0) (-1.6,0) (0,0,) (3,0)
y-intercept: (0,0)
End behavior:
x --> +∞, y --> +∞ and x--> -∞, y-->+ ∞
Vertical shrink: 0.2
Positive "a" value
Degree: 4 (even)
In 1990, the population of Denver was 470 thousand. In 2000, the population was 555 thousand. Write a function for exponential growth if t(0)=470 and t(10)=555
y=x3+4x2-3x-2
Given x=1 is one of the x-intercepts, find the other two
(-4.5,0)
(-0.4,0)
x2+4=0
Given the function, what is the number of real roots and the number of complex roots?
Real Roots: 0
Complex Roots: 2
Total number of roots: 2
f(x)=x3-11x
Find the roots
x= 3.32
x=-3.32