graph the function $y=x^3+3x^2-1$. based on the graph, what is the least possible $x$-value if $y=0$? round your answer to the nearest hundredth, if necessary.

-2.88
-2.00
-0.65
-0.53

Question

graph the function $y=x^3+3x^2-1$. based on the graph, what is the least possible $x$-value if $y=0$? round your answer to the nearest hundredth, if necessary.

-2.88
-2.00
-0.65
-0.53

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Cubic Function Properties", "Polynomial Roots" ], "new_concepts": [], "current_concepts": [ "Cubic Function Properties", "Polynomial Roots", "Graphical Solutions" ] } ## Evaluate the function at the given options $$ \begin{aligned} f(-2.88) &= (-2.88)^3 + 3(-2.88)^2 - 1 \ &= -23.887872 + 24.8832 - 1 \ &= -0.004672 \approx 0 \end{aligned} $$ ## Verify other roots to find the least x-value $$ \begin{aligned} f(-2) &= (-2)^3 + 3(-2)^2 - 1 = 3 e 0 \ f(-0.65) &= (-0.65)^3 + 3(-0.65)^2 - 1 = -0.007625 \approx 0 \ f(-0.53) &= (-0.53)^3 + 3(-0.53)^2 - 1 = -0.306577 e 0 \end{aligned} $$ ## Identify the least real root $$ x \approx -2.88 < -0.65 $$

(A) -2.88

(B) -2.00

(C) -0.65

(D) -0.53

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QUESTION IMAGE

Question

Explanation:

Evaluate the function at the given options

Verify other roots to find the least x-value

Identify the least real root

Answer: