Define Quadratic Function

Introduction to define quadratic function:

Quadratic function is defined as a polynomial function which is of the form f(x) = ax^2 + bx + c, a ? 0. The quadratic function is also called as second order polynomial function or polynomial function of degree 2. When the quadratic function is set to zero, then it becomes quadratic equation. In this article, we are going to see various forms and roots of quadratic function with example problems which help you to learn quadratic function.

Define Various Forms of Quadratic Function:

General form:

The general form of quadratic function is defined by f(x) = ax^2 + bx + c

Vertex form:

The vertex form of quadratic function is defined by f(x) = a(x - h)^2 + k, where h and k are the coordinates.

Factor form:

The factor form of quadratic function is defined by f(x) = a(x - x_1)(x - x_2), where x_1 and x_2 are the roots of the quadratic equation.

Define Roots of Quadratic Function:

The roots of quadratic function f(x) = ax^2 + bx + c can be obtained by equating the quadratic function to zero and solve it for x. When the coefficients of the quadratic function such as a, b and c are real or complex, then the roots of quadratic function is given by

x = '(-b +- sqrt(b^2 - 4ac))/(2a)' .

The above formula is called as quadratic formula to find solution to the quadratic equation.

Example problem to find roots of quadratic function:

Find the roots of the quadratic function f(x) = x^2 + 18x + 23 = 0.

Solution:

Step 1: Given equation

x^2 + 18x + 80 = 0

Step 2: Consider the variables

a = 1

b = 18

c = 23

Step 3: Substitute all values in the quadratic formula

x = '(-b +- sqrt(b^2 - 4ac))/(2a)'

x = '(-18 +- sqrt(18^2 - 4(1)(23)))/(2(1))'

Step 4: Solve the above equation for x

x = '(-18 +- sqrt(324 - 92))/(2)' .

x = '(-18 +- sqrt(232))/(2)' .

x = '(-18 +- 15.231)/(2)' .

x = '(-18 + 15.231)/(2)' , '(-18 - 15.231)/(2)' .

x = - 1.384, - 16.615

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Step 5: Solution

x = - 1.384, - 16.615

by: Smith

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