the quadratic function (d = -2x^2 + 15) models a skateboarders distance, in feet, from the bottom of a hill (x) seconds after the skateboarder starts moving down the hill. after how many seconds is the skateboarder 8 ft from the bottom of the hill?

a. 0.9 s
b. 1.9 s
c. 3.4 s
d. 3.9 s

Question

the quadratic function (d = -2x^2 + 15) models a skateboarders distance, in feet, from the bottom of a hill (x) seconds after the skateboarder starts moving down the hill. after how many seconds is the skateboarder 8 ft from the bottom of the hill?

a. 0.9 s
b. 1.9 s
c. 3.4 s
d. 3.9 s

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Word Problems", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Quadratic Word Problems", "Solving Quadratic Equations" ] } ## Set up the equation with the given distance $$ \begin{aligned} d &= -2x^2 + 15 \ 8 &= -2x^2 + 15 \end{aligned} $$ ## Solve for x squared $$ \begin{aligned} -2x^2 &= 8 - 15 \ -2x^2 &= -7 \ x^2 &= 3.5 \end{aligned} $$ ## Calculate the positive time value $$ \begin{aligned} x &= \sqrt{3.5} \ x &\approx 1.87 \text{ s} \approx 1.9 \text{ s} \end{aligned} $$

(A) 0.9 s

(B) 1.9 s

(C) 3.4 s

(D) 3.9 s

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Word Problems" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the equation with the given distance

Solve for x squared

Calculate the positive time value

Answer: