Chapter 9, Problem 25GR

To determine

To find: The definition of quadratic polynomial to make a conjecture with the definition of a quadratic function.

Answer to Problem 25GR

When two straight line equation or linear expression by multiplying and it will give the product of quadratic function.

Explanation of Solution

Given:

Quadratic polynomial and quadratic function.

Concept used:

A polynomial functon with degree two is called quadratic function.

All quadratic equation forms a image of parabola.

A quadratic function represent as the product fo the linear expresions.

A quadratic function has the same $x$ intercepts as it is linear components $y$ intercept.

Calculation:

A polynomial functon with degree two is called quadratic function.

All quadratic equation forms a image of parabola.

A quadratic function represent as the product fo the linear expresions.

A quadratic function has the same $x$ intercepts as it is linear components $y$ intercept.

Example:

  $\begin{array}{l}\left(x+3\right)\left(x+2\right).\\ \Rightarrow x^2+2x+3x+6.\\ \Rightarrow x^2+5x+6.\end{array}$

Hence, when two straight line equation or linear expression multiply each other it will give the product of quadratic function.