is the function written in vertex or standard form?

(f(x) = -(x - 1)^2 + 4)

vertex
standard

Question

is the function written in vertex or standard form?

(f(x) = -(x - 1)^2 + 4)

vertex
standard

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Standard Form of a Quadratic", "Vertex Form of a Quadratic" ], "new_concepts": [], "current_concepts": [ "Standard Form of a Quadratic", "Vertex Form of a Quadratic" ] } ## Identify the given function The given function is: $$f(x) = -(x - 1)^2 + 4$$ ## Compare with quadratic forms Using the **Vertex Form of a Quadratic** and **Standard Form of a Quadratic** knowledge points: Using the *Vertex Form of a Quadratic* and *Standard Form of a Quadratic* knowledge points $$ \begin{aligned} &\text{Vertex Form: } f(x) = a(x - h)^2 + k\ &\text{Standard Form: } f(x) = ax^2 + bx + c \end{aligned} $$ ## Determine the form of the function Using the *Vertex Form of a Quadratic* knowledge point $$ \begin{aligned} &f(x) = -(x - 1)^2 + 4 \text{ matches } a(x - h)^2 + k\ &\text{where } a = -1, \quad h = 1, \quad k = 4 \end{aligned} $$

Vertex

Standard

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex Form of a Quadratic" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given function

Compare with quadratic forms

Determine the form of the function

Answer: