Final Review

Quadratics

100

Factor completely, then solve:

y²-36=0

(y-6)(y+6)=0

y=-6,6

200

Solve:

7x²+18x+15=0

-18+- 2sqrt6i / 7

300

What's the x- and y-intercepts?

y=x²-10x+9

x-int:(9,0),(1,0)

y-int:(0,9)

400

Rewrite in vertex form, and reveal the vertex:

y=x²-4x+13

y=(x-2)²+9

V: (2,9)

500

Factor completely:

x³-2x²-25x+50

(x-5)(x+5)(x-2)

Polynomials

100

Express both end behavior limits using limit notation:

f(x)=(x²+13)(2x³-x⁴)(x⁷+3x²)

Show on board

200

Identify roots and the root behavior:

(x-3)²(x+2)⁷(x+5)

(3,0)(b), (-2,0)(c), (-5,0)(c)

300

Use the remainder theorem to solve:

x⁷+6x⁶+3x⁵-9x⁴+4x³+5x²+2x+1/(x+1)

-7

400

Use synthetic division to solve:

x⁴+3x³+5x+6/(x+6)

x³-3x²+18x-103+ 624/x+6

500

Use long division to divide:

(x⁴+5x²+7x+3)/(x+3)

x³-3x²+14x-35+108/x+3

Exponentials

100

Convert to logarithmic form:

6³=216

log₆216=3

200

Rewrite in exponential form:

⁷sqrt(x⁶)

x^6/7

300

Evaluate:

log₅³sqrt(25)

x=2/3

400

Evaluate:

log₅(1/125)

x=-3

500

Solve the equation:

log₂x+log₂(x-6)=4

x=8 

x=-2

Trigonometric

100

What is tan(7𝜋/4)

-1

200

What's the value of:

sec(600^o)

-2

300

What's the two trig equations for a graph?

x=asin(bx)+d

x=acos(bx)+d

400

Evaluate sin^-1(cos(7𝜋/4))

𝜋/4

500

Solve:

2cos(x)+sqrt 3 = 0 given that 0<x<2𝜋

5𝜋/6

7𝜋/6

Rational Functions

100

Simplify:

10x⁴+50x³+60x²/5x³

2(x+3)(x+2) / x

200

Solve:

x/x-4 + 1/x-9 = 5/x²-13x+36

x=9

x=-1

300

What are the horizontal asymptotes?

h(x)=32x²/8x²-5

y=4

400

Describe the VA(s) and hole(s) of the graph:

y=(x-5)(x-2)/(x-2)(x+4)

Hole(s)

x=2

y= -1/2

(2,-1/2)

VA: x=-4

500

At x=-9, the function h(x)= x²+x-72/x²+13x+36 has a(n)

1.) VA

2.) HA

3.) Removable Discontinuity 

4.) X-intercept

Removable Discontinuity 

hole: x=-9