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Quadratic Polynomials

Quadratic Polynomials and Functions (Definition)

We assume that you are familiar with expanding the product of two linear functions:

(x + a)(x + b)

A quadratic polynomial in x is an expression of the form ax2 + bx+ c, where a 0.

Here are some examples:

x2x − 2

x2 − 1

2x2 + x + 1

(x − 2)(x − 3) = x2 − 5x + 6

A quadratic function is a function of the form y = ax2 + bx+ c, where a 0.

We first look at functions of the form y = ax2.
Since x2 ≥ 0 for any x, the value of y = ax2 has the same sign as a.

a
y = x2

x = -2

x = -1
x = 0
x = 1
x = 2
-2
y = -2x2
-8
-2
0
-2
-8
-1
y = -x2
-4
-1
0
-1
-4
1
y = x2
4
1
0
1
4
2
y = 2x2
8
2
0
2
8

Note that at each x-value, the magnitude of y = ax2 grows as the magnitude of a grows.

 


Quadratic Polynomials Index | Graphs of Quadratic Functions >>

 

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