Precalculus

• Rational Number


  -any number that is a real number that can be written ass a terminating or repeating decimal
• Irrational Number


  -real number that cannot be written as a terminating or repeating decimal (square root of 5)
• Quadratic Formula

  -b±[√b²-4ac]/2a
• Factoring Cubes

  a^3+b^3=(a+b) (a^2-ab+b^2)-if it is A^3-B^3 then change to (a-b)(a^2+ab+b^2)
• Discriminant


  -for quadratic expression, the discriminant is b^2-4ac-determines tht nature of the roots when the quadratic equation=0-if discriminant is greater than 0, 2 real roots -if discriminant=0, 1 real root -if discriminant is less than 0, 2 imaginary roots
• Discriminant with x intercepts

  -greater than 0, 2 x intercepts -equal to 0, the vertex lies on the x axis -less than 0, the parabola doesn't intersect the x axis
• Given roots to quadratic equation and have to find the original equation

  -formula is X^2-(sum of roots)x+(product of roots)=0
• Distance Formula

  d = √[( x₂ - x₁)² + (y₂ - y₁)²]
• Midpoint Formula


  (x₁+x₂)/2, (y₁+y₂)/2-is coordinate set
• Circle with center at origin

  X^2+Y^2=R^2

  
• Circle with center at (h,k)


  (X-h)^2 +(y-k)^2=r^2-if a line is tangent to a circle, the line is perpendicular to the radius drawn to the point of tangency
• Slope intercept form

  y=mx+b-m=slope -b=y intercept
• point slope form


  y-y1=m(x-x1)-passes through point (x1,y1)
• standard form


  ax+by=c
• Parallel Lines


  -have equal slopes
• Perpendicular Lines


  -have slopes that are opposite and reciprocal
• Constant of proportionality with K


  look at other slides
• Y=Kx

  -y varies as x -y varies directly as x -y is directly proportional to x
• Y=K/x

  -y is inversely proportional to x
• Y=kxz

  -y varies jointly as x and z
• Y=Kx/z

  -y varies directly as x and inversely as z
• Y=Kx+b

  -y varies linearly as x
• relation


  - a set of ordered pairs
• function


  - a relation in which each input has a unique output
• domain


  -the set of input values
• range


  -the set of corresponding output values
• zeros

  -the input values that make the output zero-values for which f(x)=0-located on the x axis
• Vertical Line test


  a relation is a function and passes the vertical line test if when a vertical line is drawn through the graph, it touches the graph only ONE time.
• Constant


  f(x)=a
• Linear


  f(x)=ax+b
• Quadratic


  f(x)=ax^2+bx+c
• Cubic


  f(x)=ax^3+bx^2+cx+d
• Quartic


  f(x)=ax^4+bx^3+cx^2+dx+e
• Triangle


  A=(B)(H)/2- formula is one half base times hight
• Rectangle


  A=bh
• Parallelogram


  A=bh
• Trapezoid


  A=(1/2)(B+b)(H)
• Circle


  A=@r^2@=pie C=2(pie)r or (pie)(diameter)
• Prisms


  V=(area of base)(height)
• Pryamids


  V=(1/3)(area of base)(height)