Important Equations
Important Definitions
Graphs, Relations, and Functions
One Variable and Literal Equations
Solving Quadratic Equations
100
What is the Pythagorean Theorem?
a^2+b^2=c^2
100
What is a function?
A function is a relation with one unique output (y-value) for every input (x-value).
100
Find the length and midpoint M of the line segment joining (-4,5) and (6,-2).
d=sqrt(149) units Midpoint = (1,3/2)
100
Solve the following equation analytically (using algebra): 2x+3=(4/3)(x+1)
x=(-5/2)=-2.5
100
Simplify the following radical: sqroot(-50x)
5i*sqroot(2x)
200
What is the Midpoint Formula?
([X1+X2]/2, [Y1+Y2]/2)
200
What is the standard form of a quadratic equation?
ax^2+bx+c=0
200
What is the domain restriction of the following expression: 1/sqroot(A-4)
A>4
200
Solve the following equation for z: Ax+B(y-z)=C
z=y-(C-Ax)/B
200
Find the exact value of the following: i^9
i=sqroot(-1)
300
What is the distance formula?
d=sqroot[(y2-y1)^2+(x2-x1)^2]
300
What are two non real numbers discussed in class and what is the exact value of one of them?
Imaginary numbers and infinity. i=sqroot(-1)
300
Complete the square to find the circle and radius of the circle: x^2-6x+y^2+8y=0
Center: (3,-4) Radius: 5
300
Solve the following equation using a graphing calculator and the intersect method: 1.5x+2(x-3)=-5.5(x+9)
x=-4.8
300
Perform the following operations and simplify the result: (-2+3i)/(4-5i) Hint: you need to use a complex conjugate
(2i-23)/41
400
What is the equation of a circle?
(x-h)^2+(y-k)^2=r^2
400
Define a conditional equation, a contradiction, and an identity.
A conditional equation is an equation that is true given a certain condition. A contradiction is an equation that has no real numbers as the solution set. An identity is an equation that has all real numbers as the solution set.
400
Write the equation for the circle with center at (3,-4) and radius 8.
(x-3)^2+(y+4)^2=64
400
What is the least common denominator (LCD) of the following rational equation and what values can x NOT be?
LCD: x+2 X cannot equal -2
400
Solve the following using any of the appropriate methods we have learned in class to solve quadratic equations: x^2-5x=x-7
X=7,-1
500
What is the quadratic formula?
x=[-b+/-sqrt(b^2-4ac)]/2a
500
What is the expression known as "the determinant?"
b^2-4ac
500
Given f(x)=2x^2+3x-1 Find f(a+1) and simplify.
2a^2+6a+4
500
Solve the following with a graphing calculator using the intercept method: 0.06x+0.2=x-1
x=1.27
500
Write a quadratic equation that has the solution set {2,5}.
x^2-7x+10=0
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