PRECALCULUS Study Questions with Answers Rational Number - Answer --any number that is a real number that can be written ass a terminating or repeating decimal Irrational Number - Answer --real numbe r that cannot be written as a terminating or repeating decimal (square root of 5) Quadratic Formula - Answer --b±[√b² -4ac]/2a Factoring Cubes - Answer -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 - 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 - Answer -d = √[( x₂ - x₁)² + (y₂ - y₁)²] Midpoint Formula - Answer -(x₁+x₂)/2, (y₁+y₂)/2 -is coordinate set Circle with center at origin - Answer -X^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 - Answer -y=mx+b -m=slope -b=y intercept point slope form - Answer -y-y1=m(x -x1) -passes through point (x1,y1) standard form - Answer -ax+by=c Parallel Lines - Answer --have equal slopes Perpendicular Lines - Answer --have slopes that are opposite and reciprocal Constant of proportionality with K - Answer -look at other slid es 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 - Answer -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 - Answer -f(x)=a Linear - Answer -f(x)=ax+b Quadratic - Answer -f(x)=ax^2+bx+c
formula is X^2-(sum of roots)x+(product of roots)=0 Distance Formula - Answer -d = √[( x₂ - x₁)² + (y₂ - y₁)²] Midpoint Formula - Answer -(x₁+x₂)/2, (y₁+y₂)/2 -is coordinate set Circle with center at origin - Answer -X^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 - Answer -y=mx+b -m=slope -b=y intercept point slope form - Answer -y-y1=m(x -x1) -passes through point (x1,y1) standard form - Answer -ax+by=c Parallel Lines - Answer --have equal slopes Perpendicular Lines - Answer --have slopes that are opposite and reciprocal Constant of proportionality with K - Answer -look at other slid es 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 - Answer -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 - Answer -f(x)=a Linear - Answer -f(x)=ax+b Quadratic - Answer -f(x)=ax^2+bx+c
