Unit 4: Algebra II

The possible number of intersection points of two different ellipses range from ___ to as many as four.

0

When finding the solution to a system of equations, it is important to find ___ solutions.

all

The quadratic formula can be used to find the roots of ___ quadratic equation.

any

A(n) ___ number is a number of the form a+bia+bi where aa and bb are real numbers and i2=−1.i2=-1.

complex

The ___ of a complex number a+bia+bi is the complex number a−bi.a-bi.

conjugate

If an inequality contains the less than symbol (<), its graph would be a ___ line.

dashed

If the coefficient in front of the x2 in a quadratic equation is negative, the parabola will curve ___.

down

To find the value of yy using the value of x,x, use ___ equation of the system.

either

The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, b2−4ac, is ___.

either positive or zero

__ is not a technique that should be used every time to solve quadratic equations.

factoring

The quadratic ___ calculates the roots of a quadratic equation and indicates the nature of its graph.

formula

Any point that is on a ___ is a solution.

graph

If the parabola intersects the xx -axis at two points, the axis of symmetry will be ___ between the two points of intersection.

halfway

A(n) ___ number is a number of the form bibi where bb is a real number, and i2=−1.i2=-1.

imaginary

Complex numbers are represented on a Cartesian coordinate system with a horizontal real axis and a vertical ___ axis.

imaginary

If the discriminant is ___, a quadratic will have no real number roots and will not intersect the xx -axis at all.

negative

If the value under the square root sign in the quadratic equation is negative, there are ___ xx -intercepts.

no

The graphs of a line and parabola could intersect at one point, two points, or ___.

no points

To find the solution area of the graph of an inequality, chose a point ___ the curve and determine if it is a part of the solution.

not on

If the discriminant, b2−4ac is ___, a quadratic will have two real roots, two points of intersection with the xx -axis.

positive

When we combine complex numbers, we combine the ___ parts, then combine the imaginary parts.

real

The solutions to a quadratic equation are called the ___ or x-intercepts.

roots

If an inequality contains the symbols, ≤ or ≥ it would be graphed as a ___ line.

solid

Any value or values for a variable or variables that make an equation or inequality true is called a ___

solution

A ___ is a quantity that has both length and direction.

vector

If the discriminant is ___, there will be one real number root and the vertex of the quadratic will be on the xx -axis.

zero