the vertex form of the equation of a parabola is $y = (x - 4)^2 + 22$.
what is the standard form of the equation?

a. $y = x^2 - 8x + 38$
b. $y = x^2 + x + 11$
c. $y = x^2 + 8x + 22$
d. $y = 4x^2 - 8x + 38$

Question

the vertex form of the equation of a parabola is $y = (x - 4)^2 + 22$.
what is the standard form of the equation?

a. $y = x^2 - 8x + 38$
b. $y = x^2 + x + 11$
c. $y = x^2 + 8x + 22$
d. $y = 4x^2 - 8x + 38$

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 $$ (x - 4)^2 = x^2 - 8x + 16 $$ ## Substitute and simplify the equation $$ \begin{aligned} y &= (x^2 - 8x + 16) + 22 \ y &= x^2 - 8x + 38 \end{aligned} $$

A. $y = x^2 - 8x + 38$

B. $y = x^2 + x + 11$

C. $y = x^2 + 8x + 22$

D. $y = 4x^2 - 8x + 38$

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

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Question

Explanation:

Expand the squared binomial

Substitute and simplify the equation

Answer: