Quadratic Functions
The coordinates of the vertex of
f(x) = -0.5x2 - 2x - 5.
What is (-2, -3)?
(2+3i)+(−8+i)
What is −6+4i?
What is the end behavior of the polynomial?
f(x)=10x2−23x+50
x→−∞,f(x)→∞
x→∞,f(x)→∞
How many zeros does the polynomial have?
f(x)=2x5+4x3−8x2
What is 5?
Determine the vertical asymptotes and holes (removable points of discontinuity) of the rational function shown below.
f(x)=(x−1)(x−2) / (x−1)(x+7)
Holes at x=1
Vertical Asym. at x=-7
The number of pianos produced and sold that will maximize the profit of
P(x) = -1.5x2+5100x +6000, where x is the number of pianos produced and sold and P(x) is the profit, in dollars.
What is 1700 pianos?
(12−3i)−(5−4i)
What is 7 + i?
Find the degree, leading term, leading coefficient, constant term, and end behavior of the given polynomial.
g(x)=−2x2+5x9−3x+6
What is 9?
What is 5x9?
What is 5?
What is 6?
x→−∞,g(x)→-∞
x→∞,g(x)→∞
List the possible rational roots of:
f(x)=x3+6x2−9x−14
What is ±1,±2,±7,±14 ?
Find the domain of the given function. Enter the solution using interval notation.
f(x)= x+8 / x2−9x−10
what is (−∞,−1)∪(−1,10)∪(10,∞) ?
describe the transformations that take place on f(x)=x2 to get
g(x)=4(x+7)2 -2
What is Shift left 7 units
Shift down 2 units
Vertical stretch by a factor of 4?
√−50
What is 5i√2?
Identify the zeros of f(x)=−(x+10)(x+2)2(x−9) and their multiplicity. (Smallest to Largest)
x=-10 mul. 1
x=-2 mul. 2
x=9 mul. 1
Is x+2 a factor of the polynomial?
f(x)=x4+10x3−24x2+20x+44
No; f(-2) = -156
Find the horizontal asymptote or oblique asymptote.
f(x)= (−3x+3x3−4) / (−x3+x2+5)
Horizontal Asym. at y=-3
The maximum revenue, in dollars, where x is the price of each hot dogs if
R(x) = -100x2+600x+1500.
What is $2400?
(3−2i)(5+4i)
What is 23+2i?
Divide 2x4−6x3−12x2+15x+4 by x−4
(answer will be in quotient)
What is 2x3+2x2−4x−1?
If (x-4) is a factor of
f(x)=x3+4x2−25x−28
find the remaining zeros to rewrite in factored form
What is (x−4)(x+1)(x+7) ?
Find the horizontal asymptote or oblique asymptote.
f(x)= (x2+6x+3) / (x+2)
Function: y=(x+1)2 −1
Does the parabola open up or down?
Vertex (x,y)=
Equation of the Axis of Symmetry:
What is up?
What is (-1,-1)?
What is x=-1?
Divide
3+4i / 7−i
(17+31i)/50
Divide
2x3−2x2−21x−19 by x+2
2x2−6x−9+(−1/x+2)
Find all zeros of the polynomial:
f(x)=x3+6x2−9x−14
x=−1,−7,2
Let f(x)= (x2−2x−8) / (x2−4x−12)
Find:
a) Domain (interval notation)
b) Hole(s) at x=
c) Vertical asy. at x=
d) Horizontal asy. at y=
a) (−∞,−2)∪(−2,6)∪(6,∞)
b) x=-2
c) x=6
d) y=1