to solve the equation $-x - 3 = x^2 - 2x - 15$, you could graph the following system.

$y = -x - 3$
$y = x^2 - 2x - 15$

use the graph of this system to identify all solutions of $-x - 3 = x^2 - 2x - 15$.

-7
-3
0
4

Question

to solve the equation $-x - 3 = x^2 - 2x - 15$, you could graph the following system.

$y = -x - 3$
$y = x^2 - 2x - 15$

use the graph of this system to identify all solutions of $-x - 3 = x^2 - 2x - 15$.

-7
  -3
  0
  4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Graphical Solution of Systems", "Systems of Equations from Single Equations" ], "new_concepts": [], "current_concepts": [ "Graphical Solution of Systems", "Systems of Equations from Single Equations", "Quadratic Systems" ] } ## Identify intersection points Using the *Graphical Solution of Systems* and *Systems of Equations from Single Equations* knowledge points $$ \begin{aligned} &\text{Intersection 1: } (-3, 0)\ &\text{Intersection 2: } (4, -7) \end{aligned} $$ ## Extract x-coordinate solutions Using the *Graphical Solution of Systems* knowledge point $$ \begin{aligned} &x = -3\ &x = 4 \end{aligned} $$ ## Match with given options Using the *Graphical Solution of Systems* knowledge point $$ \begin{aligned} &\text{Selected values: } -3 \text{ and } 4 \end{aligned} $$

-7

-3

0

4

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphical Solution of Systems" ] }

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QUESTION IMAGE

Question

Explanation:

Identify intersection points

Extract x-coordinate solutions

Match with given options

Answer: