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Scientific Notation
Notation and Symbols
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
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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What the Standard Form of a Quadratic can tell you about the graph

The graphs of quadratic equations come in two varieties: smiling and frowning (see Figure 1, ). The standard form of a quadratic equation:

y = a · x 2 + b · x + c,

can tell you whether a given graph will smile or frown. If the number (or coefficient), a, multiplying the x 2 is positive then the quadratic is smiling. If the number a is negative then the quadratic is frowning.

Figure 1(a): The graph of a smiling quaratic equation opens upwards and outwards, like a smiling mouth.

Figure 1(b): The graph of a frowning quaratic equation opens downwards and outwards, like an unhappy mouth.

The appearance of the quadratic equation (smiling or frowning) is controlled by the sign of the number a.

Sign of the number a in the quadratic equation

Appearance of the graph of the quadratic equation





Table 1: Effect of sign of a on appearance of quadratic graph.

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