Honors STAG 10 Midterm

Vertex Form

The equation of a quadratic function expressed as y=a(x−h)²+k, where (h,k) is the vertex.

Axis of Symmetry

A vertical line that divides a parabola into two mirror images, represented by the equation x=h.

Quadratic Formula

The formula x=(-b±√(b²-4ac))/(2a) used to find the roots of a quadratic equation.

Discriminant

The expression Δ=b²−4ac that determines the nature of the roots of a quadratic equation.

Remainder Theorem

States that the remainder R of f(x) when divided by x−a is f(a).

Factor Theorem

States that x−a is a factor of f(x) if f(a)=0.

Radical and Exponent Conversion

The relationship am/n=√[n]{a^m} which connects radicals and fractional exponents.

Exponential Growth

Described by the function y=ab^(x-h)+k, where b>1 indicates growth.

Exponential Decay

Described by the function y=ab^(x-h)+k, where 0<b<1 indicates decay.

Logarithm

The inverse operation of exponentiation, represented as log_a(b) for the base a.

Parabola

The graph of a quadratic function.

Roots/Zeros

The solutions of the equation f(x) = 0, where the graph crosses the x-axis.

Vertex

The highest or lowest point on a parabola.

Degree of a Polynomial

The highest power of the variable in a polynomial expression.

Leading Coefficient

The coefficient of the highest degree term in a polynomial.

Continuous Compound Interest

An interest calculation method given by A=Pe^(rt) where e is Euler's number.

Change of Base Formula

The formula log_a(b)=log(b)/log(a) for converting logarithms to different bases.

Log Properties

log(a) + log(b) = log(ab),

log(a) - log(b) = log(a/b),

log(a^n) = n log(a)
logb(1) = 0

logb(b^k) = k

b^logb(k) = k

logb(x) = logc(x)/logc(b)