Circles
What is the definition of a circle?
Set of all equidistant points from some center.
Given f(x), describe the transformation of
f(x)+4
Vertical shift 4 units up
The longest chord in a circle is also called..
the diameter.
The inverse operation of square rooting is..
Squaring
What's the ratio that determines the Sin(x) for some angle x?
Opposite/Hypotenuse
If the equation of a circle is of the form
x2+bx+y2+cy=d, how do we convert it to graphing form?((x-h)2+(y-k)2=r2)
By completing the square twice!!!
Given f(x), describe the transformation of
f(x-7)
Horizontal shift 7 units to the right
What does the Inscribed Angle Theorem state?
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its central angle.
Find the inverse function of
f(x)=x+3
f-1(x)=x-3
What property in proof writing allows us to state "is congruent to itself"
The reflexive property
Describe the center and radius for the given equation.(x-3)2+(y+6)2=42
The center is at (3,-6) and the radius is 4.
Given f(x), describe the transformation of
-f(x)
Reflection over the x-axis
If 3 points on a circle are connected to make a triangle and one of its sides is the diameter, what theorem allows us to state it's a right triangle?
Semi-Circle Theorem
Find the inverse function of
f(x)=2x+3
f-1(x)=(x-3)/2
What is the Quadratic Formula and what is it used for?
haha i aint finna write the whole thing here lmao
Convert to graphing form.
x2+6x+y2+8y=0
(x+3)2+(y+4)2=52
Given f(x), describe the transformation of
3f(x)+4
Vertical stretch of 3x and a vertical shift of 4 units
If an inscribed angle measure 32 degrees, what does its central angle measure?
Nintendo 64 degrees.
Find the inverse function of
f(x)=2(x+2)^2
f-1(x)=sqrt((x/2))-2
Givena standard 52 card deck, what are the odds of drawing a heart or an Ace?
1/4+1/13-1/52=16/52
Convert to graphing form and state the center and radius.
x2+8x+y2-10y=20
(x+4)2+(y-5)2=61
The center is at (-4,5) and the radius is sqrt(61)
Given f(x), describe the transformations of
3f(x+2)+1
Vertical stretch of 3 times, horizontal shift of 2 units to the left and a vertical translation of 1 unit up.
The Intersecting Chords Theorem can be proven by what triangle similarity theorem?
Angle Angle
Give an example of a function where the inverse is NOT a function.
Anything that fails the horizontal line test.
What 1/4+1/16+1/64+1/256+..=?
1/3