martha wrote an example of a quadratic function for a homework assignment. the function she wrote is…

martha wrote an example of a quadratic function for a homework assignment. the function she wrote is shown.\n$f(x) = 5x^3 + 2x^2 + 7x - 3$\nwhat possible changes can martha make to correct her homework assignment? select two options.\n- the first term, $5x^3$, can be eliminated.\n- the exponent on the first term, $5x^3$, can be changed to a 2 and then combined with the second term, $2x^2$.\n- the exponent on the second term, $2x^2$, can be changed to a 3 and then combined with the first term, $5x^3$.\n- the constant, $-3$, can be changed to a variable.\n- the $7x$ can be eliminated.

martha wrote an example of a quadratic function for a homework assignment. the function she wrote is shown.\n$f(x) = 5x^3 + 2x^2 + 7x - 3$\nwhat possible changes can martha make to correct her homework assignment? select two options.\n- the first term, $5x^3$, can be eliminated.\n- the exponent on the first term, $5x^3$, can be changed to a 2 and then combined with the second term, $2x^2$.\n- the exponent on the second term, $2x^2$, can be changed to a 3 and then combined with the first term, $5x^3$.\n- the constant, $-3$, can be changed to a variable.\n- the $7x$ can be eliminated.

Answer

Explanation:

Step1: Recall Quadratic Function Definition

A quadratic function has the form ( f(x) = ax^2 + bx + c ) (( a \neq 0 )), where the highest degree (exponent) of ( x ) is 2. Martha's function is ( f(x) = 5x^3 + 2x^2 + 7x - 3 ), which is a cubic function (degree 3).

Step2: Analyze Each Option

  • Option 1 (Eliminate ( 5x^3 )): Removing ( 5x^3 ) leaves ( f(x) = 2x^2 + 7x - 3 ), which is quadratic. Valid.
  • Option 2 (Change ( 5x^3 )’s exponent to 2): Changing ( 5x^3 ) to ( 5x^2 ) gives ( 5x^2 + 2x^2 + 7x - 3 = 7x^2 + 7x - 3 ), a quadratic. Valid.
  • Option 3 (Change ( 2x^2 )’s exponent to 3): This would make the function ( 5x^3 + 2x^3 + 7x - 3 = 7x^3 + 7x - 3 ), still cubic. Invalid.
  • Option 4 (Change -3 to a variable): This does not reduce the degree (still has ( x^3 )). Invalid.
  • Option 5 (Eliminate ( 7x )): Removing ( 7x ) leaves ( 5x^3 + 2x^2 - 3 ), still cubic. Invalid.

Answer: 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 ).