Circles + Systems
Parabolas
Factoring
Polynomials
Jumble
100
Find the radius of the circle
(x-7)^2+(x+2)^2=9
3
100
Find the equation for a parabola with focus (5,2) and directrix
y=-4
(x-5)^2=12(y+1)
100
Factor
x^3+8
(x+2)(x^2-2x+4)
100
Find k if P(3)=5 and
P(x)=x^4-3x^3-2x^2-kx+2
k=-7
100
A box is made by cutting equal squares from each corner and folding up the sides. The volume (in terms of x) is
V(x)=x(20-2x)(12-2x)
200
Find the center of the circle
x^2+y^2-8x+2y+13=0
(4, \ -1)
200
Find the equation
(y+1)^2=-4(x-3)
200
Factor
27a^3-64b^3
(3a-4b)(9a^2+12ab+16b^2)
200
Use synthetic division to divide
2x^5-8x^4-2x^2+8x+6
by
(x-4)
Answer:
2x^4-2x+(6)/(x-4)
200
Polynomial P(x) is graphed. Solve P(x) = 2. (Solve for x)
x=-4, \ x=1, \ x=5
300
If the circle
x^2+y^2+10x+6y+30=0
is reflected over the x-axis and then shifted 3 units to the right, find the center of the new circle.
(-2, \ 3)
300
Find the directrix for the parabola
y^2-12x+2y=23
x=-5
300
Factor:
20x^2+17x+3
(4x+1)(5x+3)
300
Divide
x^3+3x^2+2x-4
by
x^2+3
Answer:
x+3-\frac{x+13}{x^2+3}
300
Find the focal width (LR)
Focal width is 4
400
Solve the system
(-1, \ 5)
or
(3, \ -3)
400
Find the vertex if
(5,-3)
is focus for
(y-k)^2=-28(x-h)
(12,-3)
400
Factor completely:
x^5-x^3-27x^2+27
(x-1)(x+1)(x-3)(x^2+3x+9)
400
The remainder of
(x^4+x^3-kx+8)/(x+2)
is 26. Find k.
k=5
400
What is the equation for a parabola whose vertex is (h,5), focus is (1,k), and directrix is
y=-3
(x-1)^2=32(y-5)
500
Ali is 2 years older than Bob. The product of their ages is 1 less that 4 times the sum. How old are they?
Bob is 7 years old.
Ali is 9 years old.
500
Write an equation for the graph that is the set of all points in the plane that are equidistant from the point
(a,b)
and the line
x=-7a
(y-b)^2=16a(x+3a)
500
Factor Completely
28xy^2+k-7x-4y^2k
(2y+1)(2y-1)(7x-k)
500
Find k so that the remainder is a constant:
(x^4+3x^2+kx+13)/(x^2-x-1)
Answer: \ k=-6
500
P(x) is graphed. Solve for x:
P(x)>x+1
Answer:
x \in(-\infty,-2)\cup(1, \ 3)