Equation Detective
Creative Conics
Pleasing Polynomials
Savored Skills
Imagine That
By my Calculations
100
The Equation for the line through the points (-2, 5) and (3, -1) in Standard From.
6x + 5y = 13
100
Does the hyperbola below open up/down or side to side?
(x - 4)2 - (y + 8 )^2 = 1
side to side
100
The equation of a line that contains the point (5, -8) and is parallel to y = 2/3 x + 17.
y + 8 = 2/3 (x - 5)
100
(a + b)2 =
a2 + 2ab + b2
100
If z = -3 - 4i ?
What quadrant contains z and
what is the value of | z |?
The 3rd quadrant.
| z | = 5
100
What is the value of -32 - i4
-9 - 1 = -10
200
Give the equation of this parabola:
y = 2(x - 1)2 - 7
200
Give an equation for the ellipse that goes through the points
(-10, 0), (10, 0), (0, 6), and (0, -6).
x2 / 100 + y2 / 36 = 1
200
What does the discriminant tell you about the nature of the roots of y = 5x2 + 7x - 12
two REAL and RATIONAL roots.
200
The solution(s) to
2x2 - 5x + 1 = 0
x = .219 and x = 2.281
200
The line 3x - 2y = 20 does NOT pass through any part of what quadrant?
The second quadrant.
200
If f(x ) = 2x2 - 3|x2 - 2|, what is the value of
f(i)
= -2 - 3|-3|
= -11
300
Give the equation(s) of any asymptotes for the function
y = (3x + 9)/ (x2 - 9)
x = 3 and y = 0
300
Find the equation of the circle through that has a diameter with endpoints (-1, 5) and (7, -1).
(x - 3)2 + (y - 2)2 = 25
300
The cubic y = x(x - 3)(x - 9) is symmetric about what point?
(4, -20)
300
Write the expression
2x3 + 3x2 - 2x
in fully factored form.
first rule of factoring: x(2x2 + 3x - 2)
Then : x(2x - 1)(x + 2)
300
What is the range of the function
f(x) = 3|x - 2| - 5?
y >= -5
300
2-1 - 43/2 =
1/2 - 8 = -7.5
400
Find the inverse of f(x) = log (x + 1) - 2
f -1 (x) = 10x + 2 - 1
400
What kind of conic section is y = 1/x ?
A Hyperbola
400
What is the lowest point on the curve
y = (x2 + 4)(x - 3)(x + 5)?
(-3.331, -159.506)
400
Find the solution to this system of equations
2x - y = 4 and
y + 9 = x(x - 2)
(-1, -6) and (5, 6)
400
When is the function f(x) = x(x+1)2(x - 2)3 >= 0?
x <= 0 or x >= 2
400
log7(7k-1) - (1 + k)
-2
500
Find the equation of a 5th degree equation that
goes to positive infinity as x gets bigger and bigger, has a double root at x = 3 and a triple root at x = -2, and has a y - intercept of (0,10).
y = 10/72 (x+2)^3 (x - 3)^2
500
Find the foci of the ellipse:
(x - 2)2 / 12 + (y + 8)2 / 28
(2, -4) and (2, -12)
500
Write a few sentences that explain why a 5th degree polynomial cannot CROSS the x-axis exactly 4 times.
A 5th degree polynomial has at most 5 distinct roots. We are given exactly 4 real roots. The remaining root cannot be real or the curve would cross the x-axis a 5th time. This remaining root cannot be imaginary because imaginary roots come in complex conjugate pairs, which would make 6 roots.
500
The circle
x2 + 16x + y2 - 6y = 0
has center at ______ and radius of ______.
(-8, 3) and radius = sqrt(73)
500
(x2 + 4)(x2 - 2x + 1) has how many distinct roots?
1
500
|107 - 710| = 10 raised to what power?
8.435327