What are Quadratic Forms?
Quadratic forms contain a variable such as the x2 term as their highest power.
There are various quadratic forms.
To view the free examples, please scroll down to the next section.
Quadratic Forms – Types
Type 1: ax2 + bx + c = 0
The “standard” quadratic form is ax2 + bx + c = 0
In the equation above, a, b, and c are positive or negative numbers.
a, b, and c can also be fractions or imaginary numbers.
So, 2x2 + 5x – 3 = 0 is an example of this quadratic form.
Note that the variable a can never be equal to zero in the quadratic form.
3x + 2 = o is not a quadratic because none of the terms are raised to the power or 2.
The standard quadratic form can be rewritten as other equations such as:
ax2 = bx + c
ax2 + bx = c
ax2 + c = bx
Type 2: x2 + bx + c = 0
When a = 1, we can write the equation as follows: x2 + bx + c = 0
So, x2 + 5x + 6 = 0 is an example of this quadratic form.
As mentioned above, the variable a can never be equal to zero in the quadratic form.
Type 3: (ax + b)(x + c) = 0
The factored form of the equation is as follows: (ax + b)(x + c) = 0
An example of this form is: (x + 1)(x – 5) = 0
Type 4: x2 + bx = 0
When c = 0, the quadratic form can be written as shown below:
x2 + bx = 0
x2 – 10x = 0 is an example of this quadratic form.
Type 5: x2 = n
When b = 0 and c = 0, the quadratic form can be written as shown below:
x2 = 4
If you wish to solve for x in the above questions, you should also see our posts on the quadratic formula and solving quadratic equations.