Martha wrote an example of a quadratic function for a homework assignment. The function she wrote is shown.

f (x) = 5x3 + 2x2 + 7x - 3

What possible changes can Martha make to correct her homework assignment? Select two options.

The first term, 5x3, can be eliminated.

The exponent on the first term, 5x3, can be changed to a 2 and then combined with the second term, 2x2.

The exponent on the second term, 2x2, can be changed to a 3 and then combined with the first term, 5x3.

The constant, - 3, can be changed to a variable.

The 7x can be eliminated.

The two correct options, to correct Martha's homework assignment are fhe first and the second:

The first term, 5x³, can be eliminated, and The exponent of the first term, 5x³, can be changed to a 2 and then combined with the second term, 2x².

Explanation:

The function she wrote is f (x) = 5x³ + 2x² + 7x - 3.

That is not a quadratic function but a cubic function.

A quadratic function is a polynomial of degree two (the highest exponent of the variable is 2), while in the given function, 5x³ + 2x² + 7x - 3, the highest exponent of the variable is three (meaning it is a polynomial of degree 3).

Then, to change the function f (x) = 5x³ + 2x² + 7x - 3 to a degree two polynomial (quadratic function) you must eliminate any term where the variable, x, appears raised to a power greater than 2.

The only term with the variable, x, raised to a power greater than 2 is 5x³, so what she must do is to eliminate that term or change the exponent.

By eliminating the term 5x³ she will get the new polynomial 2x² + 7x - 3, whose highest power is 2, being a quadratic function as desired.

By changing the exponent of the first term, 5x³, to a 2, she will get the new polynomial 5x² + 2x² + 7x - 3. In such polynomial, 5x² and 2x² are like terms, so they can be combined to obtain 7x² + 7x - 3, which is a quadratic function, as desired.

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