Use a graphing calculator to approximate the values of x that satisfy the inequality x 2 − 3 x + 3 ≤ 57 x ^ { 2 } - 3 x + 3 \leq 57 x 2 − 3 x + 3 ≤ 57 .A) ( − 6 , ∞ ) ( - 6 , \infty ) ( − 6 , ∞ ) B) ( − ∞ , ∞ ) ( - \infty , \infty ) ( − ∞ , ∞ ) C) ( − 9 , − 6 ) ( - 9 , - 6 ) ( − 9 , − 6 ) D) ( − 9 , 6 ) ( - 9,6 ) ( − 9 , 6 ) E) ( − 6 , 9 ) ( - 6,9 ) ( − 6 , 9 )

Question

Use a graphing calculator to approximate the values of x that satisfy the inequality   x 2 − 3 x + 3 ≤ 57 x ^ { 2 } - 3 x + 3 \leq 57 x 2 − 3 x + 3 ≤ 57   .A)    ( − 6 , ∞ )  ( - 6 , \infty )  ( − 6 , ∞ )  B)    ( − ∞ , ∞ )  ( - \infty , \infty )  ( − ∞ , ∞ )  C)    ( − 9 , − 6 )  ( - 9 , - 6 )  ( − 9 , − 6 )  D)    ( − 9 , 6 )  ( - 9,6 )  ( − 9 , 6 )  E)    ( − 6 , 9 )  ( - 6,9 )  ( − 6 , 9 )

Bharat Kumar Sridharan · Accepted Answer

Final Answer : E, Explanation :  Using a graphing calculator, we can graph the function $y=x^2-3x+3$ and then visually see where the graph is below the horizontal line $y=57$. This occurs for values of $x$ between approximately $-6$ and $9$. Therefore, the inequality is satisfied when $x$ is in the interval $(-6,9)$. The correct choice is $\boxed{	extbf{(E)}}$.

Use a graphing calculator to approximate the values of x that satisfy the inequality $\leq 57$ .

A) $\infty )$
B) $\infty , \infty )$
C) $(- 9, - 6)$
D) $(- 9, 6)$
E) $(- 6, 9)$

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