which value is a solution of $\frac{7}{4}x^2 - 2 = -0.5x + 4$?

$x = -2$
$x = -1$
$x = 1$
$x = 5$

Question

which value is a solution of $\frac{7}{4}x^2 - 2 = -0.5x + 4$?

$x = -2$
$x = -1$
$x = 1$
$x = 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Graphical Solution of Equations" ], "new_concepts": [], "current_concepts": [ "Graphical Solution of Equations", "Solving Quadratic Equations" ] } ## Identify the functions from the graph $$ \begin{aligned} &f(x) = \frac{7}{4}x^2 - 2 \ &g(x) = -0.5x + 4 \end{aligned} $$ ## Find the intersection points of the two graphs $$ \begin{aligned} &\text{Intersection points from the graph: } (-2, 5) \text{ and } (1.7, 3.1) \ &\text{At } x = -2: \ &f(-2) = \frac{7}{4}(-2)^2 - 2 = 7 - 2 = 5 \ &g(-2) = -0.5(-2) + 4 = 1 + 4 = 5 \end{aligned} $$ ## Verify the given options $$ \begin{aligned} &x = -2 \implies 5 = 5 \quad (\text{True}) \ &x = -1 \implies f(-1) = -0.25 e g(-1) = 4.5 \ &x = 1 \implies f(1) = -0.25 e g(1) = 3.5 \ &x = 5 \implies f(5) = 41.75 e g(5) = 1.5 \end{aligned} $$

(A) $x = -2$

(B) $x = -1$

(C) $x = 1$

(D) $x = 5$

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

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QUESTION IMAGE

Question

Explanation:

Identify the functions from the graph

Find the intersection points of the two graphs

Verify the given options

Answer: