Equations from College Algebra

What is symmetry to the y-axis?

for every point (x, y) on the graph, the point (-x, y) is also present.

What is symmetry to the x-axis?

For every point (x, y) on the graph, the point (x, -y) is also present.

What is symmetry to the origin?

For every point (x, y) on the graph, the point (-x, -y) is also present.

How do you compose functions?

(fog)(x)= f(g(x))

What is the equation for revenue, cost, and profit?

P(x)=R(x)-C(x)

What is the equation of a circle in standard form?

The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

What is the equation for the slope of a line?

(y2-y1)/(x2-x1)

What is the equation for point-slope form?

y-y1=m(x-x1)

What is the quadratic formula?

y x = (-b ± √(b² - 4ac))/(2a)

What is the equation for the axis of symmetry?

x=-b/2a

How do you find a vertex of a parabola?

(h,k) is the vertex form of a quadratic equation, where h is the x-coordinate and k is the y-coordinate.

What is the quadratic function in vertex form?

y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

How do you find the average rate of change?

f(b)-f(a)/b-a

How do you find the present value of an investment?

P=S(1+r/k)^-n

What is the future value of an investment over periods of time?

S=P(1+r/k)^kt

What is the future value with continuous compounding?

S=Pe^{rt}

What is the future value with compounding interest annually?

S=P(1+r)^t

What is the equation for a logistic function?

f(x)= C/1+ae^-bx

What is the equation for a gompertz function?

N=Ca^R^t

What is the Change-of-Base formula?

logb(x)=loga(x)/loga(b)

What is the Log of a product?

logb(MN)=LogbM+LogbN

What is the Log of a Quotient?

logb(M/N)=LogbM-LogbN

What is the Log of a power?

logb(M^k)=k*LogbM