Algebra II Chapter 4 and 5 Study Guide and Review Vocabulary

standard form

1. A linear equation is written in the form Ax+By=C, where A, B, and C are integers whose greatest common factor is 1, A(Greater than or equal to) 0, and A and B are not both zero. 2. A quadratic equation is written in the form ax^2+bx+c=0, where a,b and c are integers, a(not equal to) 0.

vertex

1. Any of the points of intersection of the graphs of the constraints that determine a feasible region. 2. The point at which the axis of symmetry intersects a parabola. 3. The point on each branch nearest the center of a hyperbola.

quadratic function

A function described by the equation..

Axis of symmetry

A line about which a figure is symmetric.

Synthetic division

A method used to divide a polynomial by a binomial.

Relative maximum

A point on a graph of a function where no other nearby points have a greater y- coordinate.

Relative minimum

A point on the graph of a function where no other nearby points have a lesser y-coordinate.

Prime polynomials

A polynomial that cannot be factored.

Polynomial in one variable ---> Picture has more than one variable.

A polynomial with only one variable on it.

Completing the square

A process used to make a quadratic expression into a perfect square trinomial.

vertex form

A quadratic function in the form y= a(x-h)^2 +k, where (h,k) is the vertex of the parabola and x=h is its axis of symmetry.

quadratic equation

A quadratic function set equal to a value, in the form ax^2+bx+c=0, where a is not equal 0.

Complex number

Any number that can be written in the form a+bi, where a and b are real numbers and i is the imaginary number.

True or False A method called FOIL method is used to make a quadratic expression a perfect square in order to solve the related equation.

False

True or False A prime polynomial has a degree that is one less than the original polynomial.

False

True or False Polynomials that cannot be factored are called polynomials in one variable.

False

True or False The equation(quadratic equation) is known as the discriminate.

False

True or False The relative maximum and relative minimum of a function are often referred to as end behavior.

False

True or False The vertex form of a quadratic function is y=a(x-p)(x-q).

False

True or False? The factored form of a quadratic equation is ax^2+bx+c=0, where a(is not equal)0 and a, b, and c are integers.

False

Square root property

For any real number n, if x^2=n, then x=(Plus or minus the square root of n).

Constant term

In f(x)= ax^2+bx+c, c is the constant term.

Discriminant

In the Quadratic Formula, the expression b^2-4ac.

Linear term

In the equation f(x) = ax^2+bx+c, bx is the linear term.

quadratic term

In the equation f(x)= ax^2+bx+c, ax^2 is the quadratic term.

End behavior

The behavior of the graph as x approaches positive infinity, or negative infinity.

Leading coefficient

The coefficient of the term with the hight degree.

Factored form

The form of a polynomial showing all its factors. y=a(x-p)(x-q) is the factored form of a quadratic equation.

Parabola

The graph of a quadratic function. The set of all points in a plane that are the same distance from a given point, called the focus, and a given line, called the directrix.

Degree of a polynomial

The greatest degree of any term in the polynomial.

FOIL Method

The product of two binomials is the sum of the products of F the first terms, O the outer term, I the inner term, and L the last term.

Depressed polynomial

The quotient when a polynomial is divided by one of its binomial factors

Quadratic formula

The solutions of a quadratic equation of the form ax^2+bx+c=0, are given by the Quadratic Formula, which is

root

The solutions of a quadratic equation.

Pure imaginary number

The square roots of negative real numbers. For any positive real number b,

zero

The x-intercepts of the graph of a function; the points for which f(x)=0.

Minimum value

The y-coordinate of the vertex of the quadratic function f(x)= ax^2+bx+c, where a>0.

Maximum value

The y-coordinate of the vertex of the quadratic function f(x)=ax^2+bx+c, where a<0.

Simplify

To rewrite an expression without parentheses or negative exponents.

True or False A point on a graph of a function where no one nearby point has a greater y-coordinate is called a relative maximum.

True

True or False Synthetic division is a shortcut method for dividing a polynomial by a binomial.

True

True or False The coefficient of the first term of a polynomial in standard form is called the leading coefficient.

True

True or False The graph of a quadratic function is called a parabola.

True

True or False To simplify an expression containing powers means to rewrite the expression without parentheses or negative exponents.

True

True or False When a polynomial is divided by one of its binomial factors the quotient is called a depressed polynomial.

True

True or False The number 6i is called a pure imaginary number.

True

True or false The axis of symmetry will intersect a parabola in one point called the parabola.

True

True or false The two number 2+3i and 2-3i are called complex conjugates.

True

Complex conjugates

Two complex numbers of the form a+bi and a-bi.

Imaginary unit

i, or the principal square root of -1.