question 2 of 10

the vertex form of the equation of a parabola is $x = (y - 4)^2 + 27$.
what is the standard form of the equation?

a. $x = y^2 + 8y + 27$
b. $x = y^2 + y + 15$
c. $x = 4y^2 - 8y + 43$
d. $x = y^2 - 8y + 43$

Question

question 2 of 10

the vertex form of the equation of a parabola is $x = (y - 4)^2 + 27$.
what is the standard form of the equation?

a. $x = y^2 + 8y + 27$
b. $x = y^2 + y + 15$
c. $x = 4y^2 - 8y + 43$
d. $x = y^2 - 8y + 43$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parabola Vertex Form", "Parabola Standard Form" ], "new_concepts": [], "current_concepts": [ "Parabola Vertex Form", "Parabola Standard Form" ] } ## Expand the squared binomial $$ (y - 4)^2 = y^2 - 8y + 16 $$ ## Substitute and simplify the equation $$ \begin{aligned} x &= (y^2 - 8y + 16) + 27 \ x &= y^2 - 8y + 43 \end{aligned} $$

A. $x = y^2 + 8y + 27$

B. $x = y^2 + y + 15$

C. $x = 4y^2 - 8y + 43$

D. $x = y^2 - 8y + 43$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parabola Standard Form" ] }

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Question

Explanation:

Expand the squared binomial

Substitute and simplify the equation

Answer: