Algebra 2 Unit 5

graph

Any point that is on a ___ is a solution.

imaginary

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

dashed

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

solid

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

negative

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

0

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

positive

If the discriminant, b^2-4ac, is ___, a quadratic will have two real roots, two points of intersection with the x -axis

0

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

false

TRUE OR FALSE: Factoring should always be used to solve quadratic equations.

false

TRUE OR FALSE: If the coefficient in front of the x^2 in a quadratic equation is negative, the parabola will curve up.

true

TRUE OR FALSE: If the parabola intersects the x-axis at two points, the axis of symmetry will be halfway between the two points of intersection.

division

The conjugate is used in ___ of complex numbers

no points

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

0

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

formula

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

any

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

either positive or zero

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, b^2-4ac, is _______

roots

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

not on

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.

either

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

all

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

real

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

complex number

a number of the form a+bi where a and b are real numbers and the set of complex numbers is designated by C

imaginary number

a number of the form bi where b is a real number, and i^2=-1

vector

a quantity that has both length and direction

solution

any value or values for a variable or variables that make an equation or inequality true

(-b/2a, -(b^2-4ac)/4a)

formula to find vertex of quadratic equation

conjugate

the conjugate of a complex number a+bi is the complex number a-bi

quadratic formula

the formula, (-b+-(sqrtb^2-4ac))/2a, used to find the solutions to a quadratic equation of the form ax^2+bx+c=y

y=a(x-h)^2+k

vertex form of a quadratic equation