INDEX
Numbers and Sets
Complex Numbers
Exponentiation
Algebraic Transformations
Functions
Discrete Algebra
Basic Formulas
Graphics of Basic Functions
Algebraic Equations and Inequalities
Ship

Basic Conceptions

Properties of Equations and Inequalities

Graphical Interpretation of Solutions

Linear Equations and Inequalities

Linear Equations

Linear Inequalities

Linear Equations and Inequalities Involving Absolute Values

Linear Equations Involving Absolute Value

Linear Equations Involving a Few Absolute Values

Linear Inequalities Involving Absolute Value

Quadratic Equations and Inequalities

Quadratic Equations
Quadratic Equations and Quadratic Functions

Extreme Value of Quadratic Function

Quadratic Formula

Solving Quadratic Equations by Factoring

Quadratic Inequalities


Extreme Value of Quadratic Function
Key Topics Remaining:   Quadratic Formula » Solving Quadratic Equations by Factoring » Quadratic Inequalities

Let a quadratic function,

y = a x2 + b x + c,

be represented by the form,

y – y0 = a ( x – x0 )2,

where    and    are coordinates of the vertex of the parabola.

  1. If  a > 0, then    for any values of  x
    and  y = y0  for  x = x0,  that is,
    is the minimum value of the quadratic function.


  2. If  a < 0, then    for any values of  x
    and  y = y0  for  x = x0,  that is,
    is the maximum value of the quadratic function.

In both cases,
is the extreme point.


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