What does the quadratic formula solve for?

The quadratic formula is specifically designed to find the values of ( x ) in a quadratic equation, which is typically expressed in the standard form ( ax^2 + bx + c = 0 ). The formula is given by

[

x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}.

]

In this context, ( a ), ( b ), and ( c ) are constants that represent the coefficients of the quadratic equation, and the solution it provides is the values of ( x ) that satisfy the equation. Therefore, when using the quadratic formula, we are looking for the values of ( x ) where the quadratic equation equals zero, confirming that the correct answer is indeed the value of ( x ).

The other choices involve finding values that are not the target variable of the quadratic formula. Coefficients ( a ) and ( b ) are constants in the equation but do not represent the solution to the equation itself. Similarly, the value of ( y ) may be derived from substituting ( x ) back into a function, but it is not directly solved by the quadratic formula.