Algebra II Simple Studies Review Terms

Algebra II review flashcards covering terms, formulas, theorems, angles, functions, trigonometry, and solving equations.

Adjacent Angles

Two angles with a common side and vertex, but no common interior points.

Absolute Value

The distance a number is from 0.

Coefficient

The number multiplied with the variable in an algebraic expression (default is 1 if unspecified).

Congruent

Equal or the same measure of an angle.

Discriminant

The number under the radical in the quadratic formula, determining the nature of the solutions.

What do different discriminant values mean for quadratic equation solutions?

Discriminant is 0: infinite solutions; positive: two real solutions; negative: no real solutions (imaginary).

Vertical Angles

Two angles whose sides form two pairs of opposite rays.

Acute Angle

An angle less than 90 degrees.

Obtuse Angle

An angle greater than 90 degrees.

Right Angle

An angle equal to 90 degrees.

Straight Angle

An angle equal to 180 degrees.

Midpoint

The point that divides a segment into two congruent segments.

Range

All of the output or y values in a function.

End Behavior

What is happening at the tails (ends) of a function.

Parabola

The graph of a quadratic function.

Ray

Part of a line with one endpoint.

Supplementary Angles

Two angles that add up to 180 degrees.

Function

A relation between inputs and outputs, where each input goes directly with one output.

Domain

All of the input or x values in a function.

Intercept

The point at which a line, curve, or surface intersects an axis.

Factor

A number or algebraic expression that divides into another expression evenly.

Reflection

A figure’s mirror image in the axis or plane of reflection.

Translation

Any transformation done to the function (shape, size, direction, or position).

Compression (Parabola)

The widening of a parabola when the A value is greater than 0, but less than 1.

Stretch (Parabola)

A thinning of the parabola when the A value becomes greater than 1.

Axis of Symmetry

The line that divides the parabola into two equal halves.

Vertex

The point where the axis of symmetry and the graph of a quadratic meet; the maximum or minimum of a parabola.

Maximum of a Parabola

The vertex of a parabola that opens downward; calculated by finding the axis of symmetry and plugging it back into the equation.

Minimum of a Parabola

The vertex of a parabola that opens upward; calculated by finding the axis of symmetry and plugging it back into the equation.

Parent Function

The simplest form of a quadratic function.

Rational Number

Any number that can be written as a fraction.

Irrational Number

A number that cannot be expressed as a fraction.

Fundamental Theorem of Algebra

Every polynomial with complex coefficients has at least one complex root; the degree of the polynomial determines its roots.

Vertical Angles Theorem

All vertical angles are congruent.

Right Angles Theorem

All right angles are congruent.

Perpendicular Bisector Theorem

A point on a perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

Angle Bisector Theorem

If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.

Triangle Midsegment Theorem

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

30-60-90 Triangle Rules

Hypotenuse = Short Leg * 2; Long Leg = Short Leg * √3; Short Leg = Hypotenuse / 2

45-45-90 Triangle Rules

Hypotenuse = Leg * √2; Leg = Hypotenuse / √2; The lengths of the two legs are equal.

Segment Addition Postulate

Given two points, the third must be on the line segment.

Ways to prove triangles are congruent

SSS, ASA, AAS, AL, SAS

Trigonometric Ratios

Sine: Opposite / Hypotenuse; Cosine: Adjacent / Hypotenuse; Tangent: Opposite / Adjacent

How to find missing angle measure

Multiply by Sine, Cosine, or Tangent to the negative power to both sides of the equation.

Translations of Functions

Translations shift the function (opposite direction for x due to the negative sign in the parent function). Add/subtract to x for horizontal shift, add/subtract to y for vertical shift.

Dilations of Functions

Multiply every coordinate point by the factor.

Reflections of Functions

Reflection over X-Axis: (x, y) -> (x, -y); Y-Axis: (x, y) -> (-x, y); y=x: (x, y) -> (y, x); y=-x: (x, y) -> (-y, -x)

Rotations of Functions

Rotation 90° Counterclockwise: (x, y) -> (-y, x); 180°: (x, y) -> (-x, -y); 270° Counterclockwise: (x, y) -> (y, -x)

Solving Quadratic Equations - Axis of Symmetry

Axis of Symmetry (AOS): x = (-B)/(2A); Plug AOS into the equation to find the vertex.

Solving Quadratic Equations - Y-Intercept

Y-intercept is found by plugging in zero for the X value of the equation.

Solving Quadratic Equations - A Value

Stretched: A > 1; Compressed: 0 < A < 1

Solving Quadratic Equations - Zeros

Zeros are calculated by using synthetic division or setting the equation to 0 and solving.

Solving Linear Quadratic Systems

Set the two expressions equal to each other and solve for X. Plug in both of the answers as X to find the Y coordinate.

Quadratic Word Problem Shortcuts

Maximum height is the vertex; when something hits the ground, set the equation to 0 and factor; starting height is represented by the C value.

Vertex Form: Characteristics

Vertex Form: vertex at (h, k), axis of symmetry at x = h, k is the min/max, range is K plus/minus infinity. Convert from standard form by finding the axis of symmetry and plugging it into the vertex form equation as H.

Adding/Subtracting Polynomials

Add or subtract like terms with the same powers; can line up expressions like columns in standard form or combine like terms in one long expression.

Multiplying Polynomials

Use the FOIL method (First, Outer, Inner, Last) to multiply terms.

Dividing Polynomials

Long division (used in any case) or synthetic division (coefficient of divisor must be equal to 1).

Solving Inequalities

Separate X and solve. Graph normally, shading solution set; solid line for equal to, dotted line otherwise. Flip inequality when dividing by a negative.

Factoring by Grouping

Put equation in standard form, multiply A by C, determine factors of product that add up to B, group like terms, set equations to 0, and solve for x.

Special Factoring Cases

Difference of Squares: (a-b)(a+b); Perfect Square Trinomials: (ax+b)^2 or (ax-b)^2

Removing Radicals from Denominator

Multiply the radical by itself to remove it from the denominator or multiply by the exponent needed.

Simplifying Higher Power Indexes

Break down coefficients/exponents, take out numbers based on the index. Stop when the index is higher than the power.

Exponent Rules

Product Rule: add exponents (same base); Power of a Power Rule: multiply exponents; Quotient of Powers Rule: subtract exponents; Power of a Product Rule: distribute exponent; Zero Power Rule: any base to the power of zero is 1.

Fractional Exponents

Denominator=index, exponents=numerator; Raise the fractional exponent to the opposite to cancel out.

Dividing Radical Expressions

Write as one big radical and simplify where possible. Then rationalize denominators by multiplying

Using the Powers of i

Simplify and convert it to a real number

Solving with OR

A = Probability of event A occurring.

Solving the Probability of AND(independent)

P(A and B) = P(A) x P(B)

P(B)=

Probability of event B