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The function f is defined by f(x) = (x+ 3)(x + 1).The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f ?
  • a)
    −4 < x < −3
  • b)
    −3 < x < 1
  • c)
    1 < x < 3
  • d)
    3 < x < 4
Correct answer is option 'B'. Can you explain this answer?
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The function f is defined by f(x) = (x+ 3)(x + 1).The graph of f in th...
Choice B is correct. The graph of a quadratic function in the xy-plane is a parabola. The axis of symmetry of the parabola passes through the vertex of the parabola. Therefore, the vertex of the parabola and the midpoint of the segment between the two x-intercepts of the graph have the same x-coordinate. Since f(–3) = f(–1) = 0, the x-coordinate of the vertex is = –2. Of the shown intervals, only the interval in choice B contains –2.
Choices A, C, and D are incorrect and may result from either calculation errors or misidentification of the graph’s x-intercepts.
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The function f is defined by f(x) = (x+ 3)(x + 1).The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f ?a)−4 < x < −3b)−3 < x < 1c)1 < x < 3d)3 < x < 4Correct answer is option 'B'. Can you explain this answer?
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