Precalculus Guide

PRECALCULUS GUIDE Rational Number - answer-any number that is a real number that can be written ass a terminating or repeating decimal Irrational Number - answer-real number that cannot be written as a terminating or repeating decimal (square root of 5) Quadratic Formula - answer-b±[√b²-4ac]/2a Factoring Cubes - answera^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 - answer-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 - answer-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 - answer-formula is X^2-(sum of roots)x+(product of roots)=0 Distance Formula - answerd = √[( x₂ - x₁)² + (y₂ - y₁)²] Midpoint Formula - answer(x₁+x₂)/2, (y₁+y₂)/2 -is coordinate set Circle with center at origin - answerX^2+Y^2=R^2 Circle with center at (h,k) - answer(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 - answery=mx+b -m=slope -b=y intercept point slope form - answery-y1=m(x-x1) -passes through point (x1,y1) standard form - answerax+by=c Parallel Lines - answer-have equal slopes Perpendicular Lines - answer-have slopes that are opposite and reciprocal Constant of proportionality with K - answerlook at other slides Y=Kx - answer-y varies as x -y varies directly as x -y is directly proportional to x Y=K/x - answer-y is inversely proportional to x Y=kxz - answer-y varies jointly as x and z Y=Kx/z - answer-y varies directly as x and inversely as z Y=Kx+b - answer-y varies linearly as x relation - answer- a set of ordered pairs function - answer- a relation in which each input has a unique output domain - answer-the set of input values range - answer-the set of corresponding output values zeros - answer-the input values that make the output zero -values for which f(x)=0 -located on the x axis Vertical Line test - answera 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 - answerf(x)=a Linear - answerf(x)=ax+b Quadratic - answerf(x)=ax^2+bx+c