Martha wrote an example of a quadratic function for her …

Mathematics Questions

Martha wrote an example of a quadratic function for her homework, which is f(x) = 5x¬¨‚â• + 2x¬¨‚â§ + 7x – 3. What changes can she make to correct her assignment? Select two options.

Short Answer

The degree of the expression (5x¬¨‚â• + 2x¬¨‚â§ + 7x – 3) is 3 due to the highest power being 3. To convert it into a quadratic function (degree of 2), Martha can either eliminate the (5x¬¨‚â•) term or change its exponent to 2 to combine it with (2x¬¨‚â§).

Step-by-Step Solution

Identify the Degree of the Expression

To solve the problem, first analyze the given expression: 5x¬¨‚â• + 2x¬¨‚â§ + 7x – 3. The degree of an expression is determined by its highest power. In this case, the highest power is 3, making the degree of the expression equal to 3.

Understanding Quadratic Functions

A quadratic function is specifically defined as a function with a degree of 2. To convert the given expression into a quadratic form, it is important to remove or reduce the term with the highest degree. Here are two methods to achieve this:

  • Eliminate the term with the third degree, 5x¬¨‚â•.
  • Change the degree of the term 5x¬¨‚â• to 2 and combine it with 2x¬¨‚â§.

Conclude the Correct Options

Based on the methods discussed, we can conclude the correct actions to achieve a quadratic expression. The two appropriate actions for Martha in this context are:

  • The first term, 5x¬¨‚â•, can be eliminated.
  • The exponent on the first term, 5x¬¨‚â•, can be changed to 2, allowing it to combine with 2x¬¨‚â§.

Related Concepts

Degree Of An Expression

The highest power of the variable in the expression, which determines its overall degree.

Quadratic Function

A polynomial function of degree 2, typically expressed in the standard form ax² + bx + c, where a, b, and c are constants.

Highest Power

The term in an expression that has the largest exponent, which is used to determine the degree of the expression.

Scroll to Top