find the coordinates of the vertex for the parabola defined by the given quadratic function.

(f(x) = 4x^2 + 8x + 9)

the vertex is $(-1, 5)$. (type an ordered pair.)

Question

find the coordinates of the vertex for the parabola defined by the given quadratic function.

(f(x) = 4x^2 + 8x + 9)

the vertex is $(-1, 5)$. (type an ordered pair.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Vertex of a Parabola", "Quadratic Vertex Formula" ], "current_concepts": [ "Vertex of a Parabola", "Quadratic Vertex Formula" ] } ## Identify coefficients from the quadratic function $$ \begin{aligned} &f(x) = 4x^2 + 8x + 9\ &a = 4,\quad b = 8,\quad c = 9 \end{aligned} $$ ## Calculate the x-coordinate of the vertex $$ \begin{aligned} &h = -\frac{b}{2a}\ &h = -\frac{8}{2(4)} = -1 \end{aligned} $$ ## Calculate the y-coordinate of the vertex $$ \begin{aligned} &k = f(h) = f(-1)\ &k = 4(-1)^2 + 8(-1) + 9\ &k = 4 - 8 + 9 = 5 \end{aligned} $$ The vertex is $(-1, 5)$ (Type an ordered pair.) { "elements": [ { "type": "functiongraph", "params": [ { "js": "4*x*x + 8*x + 9", "latex": "4x^2 + 8x + 9" }, -4, 2 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "f(x)", "withLabel": true } }, { "type": "point", "params": [ [-1, 5] ], "properties": { "name": "Vertex (-1, 5)", "size": 4, "color": "#F2557F", "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true, "labelPosition": "top" } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of a Parabola" ] }

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Question

Explanation:

Identify coefficients from the quadratic function

Calculate the x-coordinate of the vertex

Calculate the y-coordinate of the vertex

Answer: