question 16 of 25

which direction does the graph of the equation shown below open?

\y^2 - 4x + 4y - 4 = 0\

a. up
b. down
c. right
d. left

Question

question 16 of 25

which direction does the graph of the equation shown below open?

\y^2 - 4x + 4y - 4 = 0\

a. up
b. down
c. right
d. left

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Parabola Equation" ], "new_concepts": [], "current_concepts": [ "Parabola Equation", "Conic Sections" ] } ## Identify the conic section type $$ y^2 - 4x + 4y - 4 = 0 $$ ## Rearrange into standard form $$ \begin{aligned} y^2 + 4y &= 4x + 4\ (y^2 + 4y + 4) &= 4x + 4 + 4\ (y + 2)^2 &= 4x + 8\ (y + 2)^2 &= 4(x + 2) \end{aligned} $$ ## Determine the direction of opening $$ \begin{aligned} &(y - k)^2 = 4p(x - h)\ &4p = 4 \implies p = 1 > 0 \end{aligned} $$

A. Up

B. Down

C. Right

D. Left

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QUESTION IMAGE

Question

Explanation:

Identify the conic section type

Rearrange into standard form

Determine the direction of opening

Answer: