which system of equations can you use to find the roots of the equation?
$x^3 - 10x = x^2 - 6$

$y = x^3 - x^2 + 10x + 6$
$y = 0$

$y = x^3 - x^2 + 10x$
$y = 6$

$y = x^3 - 10x$
$y = x^2 - 6$

use the graphing calculator to graph the system. in order to view all of the solutions of this system,
dropdown menu
- use the default window
- zoom in on the graph
- zoom out on the graph

Question

which system of equations can you use to find the roots of the equation?
$x^3 - 10x = x^2 - 6$

$y = x^3 - x^2 + 10x + 6$
$y = 0$

$y = x^3 - x^2 + 10x$
$y = 6$

$y = x^3 - 10x$
$y = x^2 - 6$

use the graphing calculator to graph the system. in order to view all of the solutions of this system,
dropdown menu
- use the default window
- zoom in on the graph
- zoom out on the graph

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Systems of Non-linear Equations", "Solving Equations Graphically" ], "new_concepts": [], "current_concepts": [ "Systems of Non-linear Equations", "Solving Equations Graphically", "Polynomial Roots" ] } ## Identify the system of equations representing the given equation $$ \begin{aligned} &\text{Given equation: } x^3 - 10x = x^2 - 6 \ &\text{Let } y = \text{left-hand side and } y = \text{right-hand side:} \ &\begin{cases} y = x^3 - 10x \ y = x^2 - 6 \end{cases} \end{aligned} $$ ## Determine the required graphing calculator window adjustment $$ \begin{aligned} &\text{Find the intersection points of } y = x^3 - 10x \text{ and } y = x^2 - 6: \ &x^3 - x^2 - 10x + 6 = 0 \ &\text{Approximate roots: } x \approx -2.93, \quad x \approx 0.56, \quad x \approx 3.37 \ &\text{Corresponding } y\text{-values:} \ &y(-2.93) \approx 2.58 \ &y(0.56) \approx -5.69 \ &y(3.37) \approx 5.36 \ &\text{All solutions lie within standard default window bounds } [-10, 10] \text{ for both } x \text{ and } y. \ &\text{Therefore, use the default window.} \end{aligned} $$ ## Question 1 (A) $\begin{cases} y = x^3 - x^2 + 10x + 6 \ y = 0 \end{cases}$

(B) $\begin{cases} y = x^3 - x^2 + 10x \ y = 6 \end{cases}$

(C) $\begin{cases} y = x^3 - 10x \ y = x^2 - 6 \end{cases}$ ## Question 2 (A) use the default window

(B) zoom in on the graph

(C) zoom out on the graph

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QUESTION IMAGE

Question

Explanation:

Identify the system of equations representing the given equation

Determine the required graphing calculator window adjustment

Answer:

Question 1

Question 2