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Scientific Notation
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Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Graphing Parabolas

Standard form for a Quadratic Equation:

y = ax + bx + c, where a 0

Terms:

Parabola: U-shaped graph formed by quadratic functions.

Quadratic Term: ax

Concave Upward: a parabola that opens upward (coefficient is positive)

Concave Downward: a parabola that opens downward (coefficient is neg)

Vertex of a parabola: the highest point on a concave down parabola or lowest point on a concave up parabola.

Axis of symmetry: the vertical line that passes through vertex in a parabola.

The effects of coefficients on a quadratic system:

If a > 0 then the graph is concave upward.

If a > 0 then the graph is concave downward.

If |a| > 1 then the graph is narrower then when a = 1.

If |a| < 1 then the graph is wider then when a = 1.

c is the y -coordinate of the y -intercept of the graph.

the x -coordinate of the vertex is

The axis of symmetry is the line graphed by

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