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# Precalc 1 &2

### hyperbolas, parabolas, circles, lines, etc.

TermDefinition
y= 3x-9. What is the slope? (rise/run) up 3, over 1
midpoint formula x,y = (x1+ x2/2, y1 + y1/2)
distance formula d= square root of (x2-x1)^2 +(y2-y1)^2
definition of a circle a set of all points on a plane that are an equal distance from some fixed point
center-radius form of a circle (x-h)^2 + (y-k)^2 = r^2
(x+3)^2 +(y-1)^2=1. What is the radius, and center? Center: (-3, 1), radius: 1
x^2 + (y+5)^2 =0. What is the graph? Center = (0,-5), radius = 0
Standard form of a line Ax +By = C
is 4x^2 + 3y =12 a line? No, because there is a square in the form
Both positive and negative slopes of a line go which direction? left to right
Slope = 0 Horizontal straight line ------
Slope is undefined vertical straight line I
rise/run = y2-y1/x2-x1
point slope formula y2- y1 = m(x2-x1)
parallel lines the slope of both of the lines is the same
perpendicular the slope of the lines are reciprocal (-1/m2)
I’m looking for the equation of a line, I need… A point and a slope.
Exceptions to lines with slopes Y=b, x=a
What makes a set not a function More than 1 number as an x value (input)
Open circle indicates… Parentheses and does not include end points
Closed circle indicates Brackets and does include end points
1-1 function F and f-1 are functions
Process for inverse equations 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f-1
function notation y=f(x)
a) (1,3), (2,3), 4,5) b) (1,2), (3,4), (2,1). Which is a 1-1 function? b) (1,2), (3,4), (2,1).
(x-h) goes which direction? right
(x+h) goes which direction? left
(y-k) goes which direction? upward
(y+k) goes which direction? downward
when reflecting across y-axis, (x,y) becomes.... (-x,y)
when reflecting across x-axis, (x,y) becomes.... (x, -y)
y= I x I is symmetric about which axis y axis
y^2 = 2x is symmetric about which axis? x axis
x -> kx, where I K I <1 means... a horizontal stretch
x -> kx, where I K I >1 means... a horizontal shrink
y -> ky, where I K I >1 means... shrink vertically
y -> ky, where I K I <1 means... stretch vertically
i ^2 = -1
i^3 = -i
i^4= 1
i^5= i
equation of a parabola x^2= 4ay or 4a(y-k) = (x-h)^2
parabola: a >0 (two answers) opens up or to the right
parabola: a <0 (two answers) opens down or to the left
finding foci for an ellipse (+/- c, 0)
finding intercepts for ellipse x^2/a^2 and y^2/b^2
equation for an ellipse (x-h)^2/a^2 + (y-k)^2 /b^2 =1
equation for a hyperbola (x-h)^2/a^2 - (y-k)^2 /b^2 =1
Created by: Lyd543
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