Question
Consider this quadratic equation.
x2 + 1 = 2x – 3
Which expression correctly sets up the quadratic formula?
A.
B.
C.
D.
x2 + 1 = 2x – 3
Which expression correctly sets up the quadratic formula?
A.
B.
C.
D.
Answers
GPT-4o mini
To set up the quadratic formula, we first need to rearrange the given equation into the standard form of a quadratic equation, which is \( ax^2 + bx + c = 0 \).
Starting with the original equation:
\[ x^2 + 1 = 2x - 3 \]
We can rearrange this by moving all terms to one side of the equation:
1. Subtract \( 2x \) from both sides:
\[ x^2 - 2x + 1 = -3 \]
2. Add \( 3 \) to both sides:
\[ x^2 - 2x + 4 = 0 \]
Now we have the equation in standard form:
\[ x^2 - 2x + 4 = 0 \]
In this case, \( a = 1, b = -2, c = 4 \).
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Now, substituting \( a \), \( b \), and \( c \) into the formula, we get:
\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(4)}}{2(1)}
\]
This can be simplified to:
\[
x = \frac{2 \pm \sqrt{4 - 16}}{2}
\]
Thus, the expression that sets up the quadratic formula based on the given quadratic equation is:
\[
x = \frac{2 \pm \sqrt{4 - 16}}{2}
\]
It appears your options A, B, C, and D are missing from your message, so please provide those options if you need further assistance in selecting the correct one!
Starting with the original equation:
\[ x^2 + 1 = 2x - 3 \]
We can rearrange this by moving all terms to one side of the equation:
1. Subtract \( 2x \) from both sides:
\[ x^2 - 2x + 1 = -3 \]
2. Add \( 3 \) to both sides:
\[ x^2 - 2x + 4 = 0 \]
Now we have the equation in standard form:
\[ x^2 - 2x + 4 = 0 \]
In this case, \( a = 1, b = -2, c = 4 \).
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Now, substituting \( a \), \( b \), and \( c \) into the formula, we get:
\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(4)}}{2(1)}
\]
This can be simplified to:
\[
x = \frac{2 \pm \sqrt{4 - 16}}{2}
\]
Thus, the expression that sets up the quadratic formula based on the given quadratic equation is:
\[
x = \frac{2 \pm \sqrt{4 - 16}}{2}
\]
It appears your options A, B, C, and D are missing from your message, so please provide those options if you need further assistance in selecting the correct one!