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a) Sign of the leading coefficient\newlineb) Vertex\newlinec) Axis of symmetry\newlined) Intervals where \newlineff is increasing and where \newlineff is decreasi\newlinef) Domain and range\newlineFor the toolbar, press ALT+F1010 (PC) or ALT+FN+F1010 (Mac).\newlineB I \newlineS_ Paragraph \newlinevv Arial

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Q. a) Sign of the leading coefficient\newlineb) Vertex\newlinec) Axis of symmetry\newlined) Intervals where \newlineff is increasing and where \newlineff is decreasi\newlinef) Domain and range\newlineFor the toolbar, press ALT+F1010 (PC) or ALT+FN+F1010 (Mac).\newlineB I \newlineS_ Paragraph \newlinevv Arial
  1. Sign of Leading Coefficient: a) Sign of the leading coefficient: The leading coefficient is the number in front of the highest power of xx, which is −6-6 in this case. Since it's negative, the parabola opens downwards.
  2. Vertex: b) Vertex: The vertex form of a quadratic function is f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where (h,k)(h, k) is the vertex. For f(x)=−6(x−7)2+2f(x) = -6(x - 7)^2 + 2, the vertex is (7,2)(7, 2).
  3. Axis of Symmetry: c) Axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. For the given function, the axis of symmetry is x=7x = 7.
  4. Increasing and Decreasing Intervals: d) Intervals where ff is increasing and where ff is decreasing: Since the parabola opens downwards (a<0a < 0), f(x)f(x) is increasing to the left of the vertex and decreasing to the right of the vertex. So, ff is increasing on (−∞,7)(-\infty, 7) and decreasing on (7,∞)(7, \infty).
  5. Domain and Range: e) Domain and range: The domain of any quadratic function is all real numbers, so the domain of f(x)f(x) is (−∞,∞)(-\infty, \infty). The range is limited by the vertex since it's the highest point on the graph. The range is (−∞,2](-\infty, 2].

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