select the correct answer.

which equation could be solved using this application of the quadratic formula?
\x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-4)}}{2(1)}\

$x^2 + 1 = 2x - 3$
$x^2 - 2x - 1 = 3$
$x^2 + 2x - 1 = 3$
$x^2 + 2x - 1 = -3$

Question

select the correct answer.

which equation could be solved using this application of the quadratic formula?
\x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-4)}}{2(1)}\

$x^2 + 1 = 2x - 3$
$x^2 - 2x - 1 = 3$
$x^2 + 2x - 1 = 3$
$x^2 + 2x - 1 = -3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Functions" ], "new_concepts": [ "Quadratic Formula Application" ], "current_concepts": [ "Quadratic Functions", "Quadratic Formula Application" ] } ## Identify coefficients from the quadratic formula $$ \begin{aligned} &x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ &x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-4)}}{2(1)} \ &a = 1, \quad b = 2, \quad c = -4 \end{aligned} $$ ## Write the standard form equation $$ \begin{aligned} &ax^2 + bx + c = 0 \ &x^2 + 2x - 4 = 0 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &x^2 + 2x - 1 = 3 \implies x^2 + 2x - 4 = 0 \ &x^2 + 2x - 1 = -3 \implies x^2 + 2x + 2 = 0 \ &x^2 - 2x - 1 = 3 \implies x^2 - 2x - 4 = 0 \ &x^2 + 1 = 2x - 3 \implies x^2 - 2x + 4 = 0 \end{aligned} $$

(A) $x^2+1=2x-3$

(B) $x^2-2x-1=3$

(C) $x^2+2x-1=3$

(D) $x^2+2x-1=-3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients from the quadratic formula

Write the standard form equation

Match with the given options

Answer: