click below

click below

Normal Size Small Size show me how

# Precalc 1 &2

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

Term | Definition |
---|---|

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= | radical -1 |

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 |