Quadratic Function

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Quadratic function is a function which contains a quadratic equations. Quadratic means square. The function which has the highest degree for the variable as two is called a quadratic function. So the degree of the polynomial for a quadratic function is always 2. The general form of a quadratic function is written as ax2 + b x + c. Here x is the unknown variable and a. b. c are the constants.

Example 1: The function f(x) = x2 + 6 x + 9. Solve for x if f(x) = 0?

Solution: Given here is the quadratic function f(x) = 0

This gives x2 + 6 x + 9 = 0.

The equation can be written as x2 + 3 x +3 x + 9 = 0

Now factoring the common terms gives x (x + 3) + 3 (x + 3) = 0.

Hence (x + 3) (x + 3) = 0

Therefore, x = 3 is the solution for the function.
 
Example 2: The function f(x) = x2 + 7 x + 12. Solve for x if f(x) = 0?

Solution: Given here is the quadratic function f(x) = 0

This gives x2 + 7 x + 12 = 0.

The equation can be written as x2 + 4 x +3 x + 12 = 0

Now factoring the common terms gives x (x + 4) + 3 (x + 4) = 0.

Hence (x + 3) (x + 4) = 0

Therefore, x = -3, -4 is the solution for the function.
 
 

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