Precalculus Study Guide Practice Questions and Verified Answers
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 -formula is
original equation 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
Grade A+ | Updated
, Precalculus Study Guide Practice Questions and Verified Answers
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
Grade A+ | Updated
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 -formula is
original equation 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
Grade A+ | Updated
, Precalculus Study Guide Practice Questions and Verified Answers
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
Grade A+ | Updated
