College Algebra Study Guide Questions and Answers 2023

College Algebra Study Guide Questions and Answers 2023 Distance Formula d=sqrrt((x2-x1)^2-(y2-y1)^2) Midpoint Formula ((x1+x2)/2 , (y1+y2)/2) Slope Formula (y2-y1) / (x2-x1) Slope Intercept Form y = mx + b Equation of a Circle (x-h)^2+(y-k)^2=r^2 Difference Quotient (f(x+h)-f(x)) / h Test for Symmetry of Function with respect to the X Axis Plug in -y for y Test for Symmetry of Function with respect to the Y Axis Plug in -x forx Test for Symmetry of Function with respect to the Origin Plug in -x for x and -y for y Slope of a line perpendicular to a given function Opposite reciprocal of the slope of the given function Slope of a line parallel to a given function Same slope as given function Determine whether function is even, odd, or neither. How? Find f(-x). If it = f(x) it is even; if it = -f(x) it is odd Quadratic Equation x=(-b+&-(sqrrt. b^2-4(a)(c)))/2a Vertex Formula For X coordinate: -b/2a ; For Y coordinate: f(-b/2a) Vertex Form f(x)=a((x+2)^2)+k 5 steps to manually graph polynomials 1. Find Intercepts 2. Find if it Touches or Crosses 3. Find its End Behavior 4. Find its Near X Intercept (Zeros) Properties 5. Graph Find X Intercepts Plug in 0 for y Find Y Intercepts Plug in 0 for x Find if a polynomial touches or crosses at its zeros If zero's multiplicity is even then it touches, if it is odd then it crosses Find end behavior of a polynomial y=+x^even# = up in 1st quad. and up in 2nd quad y=+x^odd# = down in 3rd quad. and up in 1st quad y=-x^even# = down in 3rd quad. and down in 4th quad. y=-x^odd# = up in 2nd quad. and down in 4th quad. Find near X intercept properties of a polynomial Plug the zero in for x everywhere but where you found that zero and examine it's properties 5 steps to manually graph rational function 1. Find Intercepts 2. Find Zeros 3. Find its above or Below Properties 4. Find Asymtotes 5. Graph Find above or below properties of a rational function Use zeros and find if the outcome is positive or negative before, after, and between them Find vertical asymtotes of a rational function Set the denominator equal to zero Find horizontal asymtotes of a rational function TopBottom = No Horizontal Asymtote Top=Bottom = Horizontal Asym. @ The Leading Coefficiant TopBottom = Horizontal Asym. @ y=0 Find oblique asymtotes of a rational function Use Long division to find equation. Only if TopBottom by exactly one. Equation of a parabola (x-h)^2=4a(y-k): opens up (x-h)^2=-4a(y-k): opens down (y-k)^2=4a(x-h): opens right (y-k)^2=-4a(x-h): opens left Equation of an elipse ((x-h)^2/a^2)+((y-k)^2/b^2)=1: longer horizontally ((y-k)^2/a^2)+((x-h)^2/b^2)=1: longer vertically Equation of a hyperbole ((x-h)^2/a^2)-((y-k)^2/b^2)=1: longer horizontally btwn. ((y-k)^2/a^2)-((x-h)^2/b^2)=1: longer vertically btwn. Equation for asymtotes of a hyperbole (y-k) = +&- (y thing / x thing)(x-h) Equation to use the inverse of a matrix to solve a system of equations X=A^-1*B