find the range of this quadratic function.

(y = x^2 + 2x)

(-infty

Question

find the range of this quadratic function.

(y = x^2 + 2x)

(-infty < y < infty)

(-1 le y < infty)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Functions", "Parabola Vertex Identification", "Range of a Function" ], "new_concepts": [], "current_concepts": [ "Quadratic Functions", "Parabola Vertex Identification", "Range of a Function" ] } ## Find the vertex of the parabola $$ \begin{aligned} x_v &= -\frac{b}{2a} = -\frac{2}{2(1)} = -1 \ y_v &= (-1)^2 + 2(-1) = 1 - 2 = -1 \end{aligned} $$ ## Determine the direction of opening $$ \begin{aligned} a &= 1 > 0 \quad \text{(opens upward)} \end{aligned} $$ ## Determine the range of the function $$ \begin{aligned} y &\ge y_v \ y &\ge -1 \implies -1 \le y < \infty \end{aligned} $$

(A) $-\infty < y < \infty$

(B) $-1 \le y < \infty$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Range of a Function" ] }

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QUESTION IMAGE

Question

Explanation:

Find the vertex of the parabola

Determine the direction of opening

Determine the range of the function

Answer: