Select the correct answer.

Consider this quadratic equation.
[tex]x^2+1=2 x-3[/tex]

Which expression correctly sets up the quadratic formula?
A. [tex]\frac{-(-2) \pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex]
B. [tex]\frac{-(-2) \pm \sqrt{(-2)^2-(1)(4)}}{2(2)}[/tex]
C. [tex]\frac{-2 \pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex]
D. [tex]\frac{-2 \pm \sqrt{(2)^2-4(1)(-2)}}{2(1)}[/tex]

Rewrite the given quadratic equation in the standard form: x 2 − 2 x + 4 = 0 .
Identify the coefficients: a = 1 , b = − 2 , c = 4 .
Substitute the coefficients into the quadratic formula: x = 2 ( 1 ) − ( − 2 ) ± ( − 2 ) 2 − 4 ( 1 ) ( 4 ) ​ ​ .
The correct expression is: 2 ( 1 ) − ( − 2 ) ± ( − 2 ) 2 − 4 ( 1 ) ( 4 ) ​ ​ ​ .

Explanation

Rewrite the equation First, we need to rewrite the given quadratic equation in the standard form a x 2 + b x + c = 0 . The given equation is x 2 + 1 = 2 x − 3 . Subtracting 2 x from both sides and adding 3 to both sides, we get x 2 − 2 x + 4 = 0 .

Identify the coefficients Now, we can identify the coefficients a , b , and c . In the equation x 2 − 2 x + 4 = 0 , we have a = 1 , b = − 2 , and c = 4 .

Apply the quadratic formula Next, we substitute the values of a , b , and c into the quadratic formula: x = 2 a − b ± b 2 − 4 a c ​ ​ . Substituting a = 1 , b = − 2 , and c = 4 , we get: x = 2 ( 1 ) − ( − 2 ) ± ( − 2 ) 2 − 4 ( 1 ) ( 4 ) ​ ​

Select the correct option Finally, we compare the expression we obtained with the given options. The expression is 2 ( 1 ) − ( − 2 ) ± ( − 2 ) 2 − 4 ( 1 ) ( 4 ) ​ ​ which matches option A.


Examples
The quadratic formula is a powerful tool used in various fields, such as physics and engineering, to solve problems involving quadratic equations. For example, in projectile motion, the height of an object can be modeled by a quadratic equation, and the quadratic formula can be used to find the time at which the object reaches a certain height. Similarly, in electrical engineering, quadratic equations can arise in circuit analysis, and the quadratic formula can be used to find the values of certain circuit parameters.

Answered by GinnyAnswer | 2025-07-03

The correct expression that sets up the quadratic formula for the equation x 2 + 1 = 2 x − 3 is option A: 2 ( 1 ) − ( − 2 ) ± ( − 2 ) 2 − 4 ( 1 ) ( 4 ) ​ ​ .
;

Answered by Anonymous | 2025-07-04