Question

martha wrote an example of a quadratic function for a homework assignment. the function she wrote is shown.
$f(x) = 5x^3 + 2x^2 + 7x - 3$
what possible changes can martha make to correct her homework assignment? select two options.

• the first term, $5x^3$, can be eliminated.
• the exponent on the first term, $5x^3$, can be changed to a 2 and then combined with the second term, $2x^2$.
• the exponent on the second term, $2x^2$, can be changed to a 3 and then combined with the first term, $5x^3$.
• the constant, $-3$, can be changed to a variable.
• the $7x$ can be eliminated.

Explanation:

A quadratic function has the form \( f(x)=ax^{2}+bx + c\) (where \(a
eq0\)), meaning the highest degree (exponent) should be 2.

• Option 1: Eliminating \(5x^{3}\) (the cubic term) leaves a quadratic function (\(f(x)=2x^{2}+7x - 3\)), so this works.
• Option 2: Changing the exponent of \(5x^{3}\) to 2 gives \(5x^{2}\), which can be combined with \(2x^{2}\) to form a quadratic term (\(7x^{2}\)), resulting in a quadratic function (\(f(x)=7x^{2}+7x - 3\)), so this works.
• Option 3: Changing the exponent of \(2x^{2}\) to 3 would create a cubic function (highest degree 3), not quadratic, so this is incorrect.
• Option 4: Changing the constant to a variable does not affect the degree (highest exponent) of the function, so it remains cubic, incorrect.
• Option 5: Eliminating \(7x\) still leaves a cubic term (\(5x^{3}\)), so the function is still cubic, incorrect.

Answer:

A. The first term, \(5x^{3}\), can be eliminated.
B. The exponent on the first term, \(5x^{3}\), can be changed to a 2 and then combined with the second term, \(2x^{2}\).