what are the roots of the equation $-3(x - 2)^2 + 13 = 0$? round the roots to two decimal places, if necessary.

$x \approx 0.08$ or $x \approx -4.08$
$x \approx -3.27$ or $x \approx 5.61$
$x \approx -1.96$ or $x \approx 2.37$
$x \approx -0.08$ or $x \approx 4.08$

Question

what are the roots of the equation $-3(x - 2)^2 + 13 = 0$? round the roots to two decimal places, if necessary.

$x \approx 0.08$ or $x \approx -4.08$
$x \approx -3.27$ or $x \approx 5.61$
$x \approx -1.96$ or $x \approx 2.37$
$x \approx -0.08$ or $x \approx 4.08$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Finding Roots" ], "new_concepts": [ "Solving Quadratic Equations in Vertex Form" ], "current_concepts": [ "Finding Roots", "Solving Quadratic Equations in Vertex Form" ] } ## Isolate the squared term $$ \begin{aligned} -3(x - 2)^2 + 13 &= 0 \ -3(x - 2)^2 &= -13 \ (x - 2)^2 &= \frac{13}{3} \end{aligned} $$ ## Solve for x $$ \begin{aligned} x - 2 &= \pm\sqrt{\frac{13}{3}} \ x &= 2 \pm \sqrt{\frac{13}{3}} \end{aligned} $$ ## Calculate decimal approximations $$ \begin{aligned} \sqrt{\frac{13}{3}} &\approx 2.081665 \ x_1 &= 2 + 2.081665 \approx 4.08 \ x_2 &= 2 - 2.081665 \approx -0.08 \end{aligned} $$

(A) $x \approx 0.08$ or $x \approx -4.08$

(B) $x \approx -3.27$ or $x \approx 5.61$

(C) $x \approx -1.96$ or $x \approx 2.37$

(D) $x \approx -0.08$ or $x \approx 4.08$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations in Vertex Form" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the squared term

Solve for x

Calculate decimal approximations

Answer: