Absolute Value Unit 1 and some other stuff
The vertex of the function:
2 l x-2 l -4
(2, -4)
The vertex of the function:
f(x)=2x2-4x+7
(1, 5)
Solve the equation.
x2+6x+9
(x+3)2
Divide using synthetic division.
(x4-5x3+3x2-8) / (x+2)
x3-7x2+17x-34+(60/x+2)
Find the sum.
3 4
_ + _
x 2x
5/x
Draw a rough graph of the function:
1/2 l x+1 l +2
l
l
l
___\____________________________/__________
\ l /
O l
l
Describe the transformation of f(x)=x2 represented by g.
g(x)=4(x-1)2+6
Right 1
Up 6
Solve the equation.
4x2+10x-24
2(2x-3)(x+4)
Describe the end behavior of the function:
-98732458x4+x+9
y -> -oo as x -> -oo
y -> -oo as x -> oo
Simplify completely.
x2+4x-12
_______
x2-36
(x-2)
____
(x-6)
Write the linear regression for the following data set as well as the r squared value and solve for x=10. Round to the nearest thousandth
x l y
1 l 8
3 l 17
4 l 25
8 l 28
15 l 41
f(x)=2.119x+10.663
r2=0.903
f(10)=31.853
Write the equation of the parabola with the following points in intercept form.
(2, 0)
(5, 3)
(6, 0)
y=-(x-2)(x-6)
x2-6x+17
x= 4+2i(sqrt2), 4-2i(sqrt2)
Subtract.
(5x5-8x4+3x2-10x+1) - (-3x5-8x3+3x2-2x+9)
8x5-8x4+8x3-8x-8
Simplify completely.
x2+x-30 2x2-2x-1
_______ / _________
x2+5x-6 x2+7x-8
2x-1
____
x+8
Describe the transformations of the function:
2 l x+2 l -2
Left 2
Down 2
f(x)=2(x-3)2-5
AOS: x=3 domain: All real numbers
vertex= (3, 5) range: y>=-5
Inc= x>3
Dec=x<3
Perform the operation. Write your answer in standard form.
(2-2i)(-8+i)
-14+18i
Factor completely.
5m3-625
5(m-5)(m2+5m+25)
Find the sum/difference.
x-3 x+4
____ -- _____
3x+6 x2-2x-8
x(x-10)
_________
3(x+2)(x-4)
A concert venue charges $200 dollars for lawn seats, 120$ for box seats, and $60 dollars to sit on the roof of the apartment building about 2 miles down the street. There are 60,000 seats total, and the total revenue for the venue was $2,760,000. There are twice as many top-of-the-apartment-building seats as there are box seats. Find the amount of seats for each type of seat.
Amount of lawn seats: 3000
Amount of top-of-the-apartment-building seats: 18000
Amount of box seats: 9000
Give the equation for the graph with the focus point of (-2, 1) and the vertex of (1, 1).
x=1/12(y-1)2+1
Solve the inequality.
x2+5x-40 > 0
x<(-5-(sqrt185))/2 or x>(-5+(sqrt185))/2
Write a polynomial function f of least degree that has a leading coefficient of 1, rational coefficients, and the given zeros.
x= -2, 3-4i
x3-4x2+13x+50
Solve for x.
-10 8
___ -- __ = -2
x+5 9
x=4