# Quadratic Equations and Expressions

Notes on Quadratic Equations and Expressions

- Created by: E.H Jane
- Created on: 25-09-12 17:49

First 227 words of the document:

IGCSEAdditional MathematicsQuadratic Equations and Expressions

Maximum/ Minimum value of a Quadratic Equation

A quadratic expression such as 2x2- 8x+ 11 or -4x2 +12x -8 has either a maximum or a minimum value.

Let's find out how we can find the extreme values for any quadratic expressions.

The expression ax2+bx+c can also be written as y =a (x-h)2+ k . This form of expression is called

complete square form.

Now how do we know whether the expression has a maximum value or a minimum value?

Writing a quadratic expression in complete square form helps us find out.

y = a(x - h)2 + k

a < 0the equation has a maximum value

a > 0the equation ha a minimum value

(h, k)turning point (it will be explained later)

kthis is the maximum or minimum value

Example: y = 2(x - 3)2 + 1

a = 2, h = 3, k = 1

a > 0 therefore, the expression has a minimum value

Since k = 1, the expression has a minimum value of 1.

You also need to know about what type of curve you will get when it is a minimum value and what type

of curve you will get when it is a maximum value.

A minimum value curve will look something like this:

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