Question

rhett is solving the quadratic equation ( 0 = x^2 - 2x - 3 ) using the quadratic formula. which shows the correct substitution of the values ( a ), ( b ), and ( c ) into the quadratic formula?

quadratic formula: ( x = \frac{-b pm sqrt{b^2 - 4ac}}{2a} )

( circ ) ( \frac{2 pm sqrt{(-2)^2 - 4(1)(-3)}}{2(1)} )
( circ ) ( \frac{-2 pm sqrt{(-2)^2 - 4(1)(-3)}}{2(1)} )
( circ ) ( \frac{2 pm sqrt{-2^2 - 4(1)(-3)}}{2(1)} )
( circ ) ( \frac{-2 pm sqrt{-2^2 - 4(1)(-3)}}{2(1)} )

Explanation:

Step1: Identify a, b, c from the quadratic equation

The quadratic equation is \(0 = x^2 - 2x - 3\), which can be written in standard form \(ax^2+bx + c = 0\). So, \(a = 1\), \(b=- 2\), \(c = - 3\).

Step2: Substitute into the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Substituting \(a = 1\), \(b=-2\), \(c=-3\) into it:

• \(-b=-(-2) = 2\)
• \(b^{2}=(-2)^{2}\)
• \(4ac = 4\times1\times(-3)\)

So the substitution gives \(\frac{2\pm\sqrt{(-2)^{2}-4(1)(-3)}}{2(1)}\)

Answer:

\(\boldsymbol{\frac{2\pm\sqrt{(-2)^{2}-4(1)(-3)}}{2(1)}}\) (the first option)