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a) Sign of the leading coefficient b) Vertex c) Axis of symmetry d) Intervals where f is increasing and where f is decreasit f) Domain and range For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). B I S_ Paragraph vv Arial

a) Sign of the leading coefficient\newlineb) Vertex\newlinec) Axis of symmetry\newlined) Intervals where f f is increasing and where f f is decreasit\newlinef) Domain and range\newlineFor the toolbar, press ALT+F1010 (PC) or ALT+FN+F1010 (Mac).\newlineB I S‾ \underline{\mathcal{S}} Paragraph ∨ \vee Arial

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Full solution

Q. a) Sign of the leading coefficient\newlineb) Vertex\newlinec) Axis of symmetry\newlined) Intervals where f f is increasing and where f f is decreasit\newlinef) Domain and range\newlineFor the toolbar, press ALT+F1010 (PC) or ALT+FN+F1010 (Mac).\newlineB I S‾ \underline{\mathcal{S}} Paragraph ∨ \vee Arial
  1. Leading Coefficient Determination: a) Sign of the leading coefficient is determined by the number in front of the (x−7)2(x - 7)^2 term.\newlineCalculation: The leading coefficient is −6-6.
  2. Vertex Calculation: b) Vertex is found by looking at the form of the equation, which is in vertex form f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where (h,k)(h, k) is the vertex.\newlineCalculation: The vertex is (7,2)(7, 2).
  3. Axis of Symmetry: c) Axis of symmetry is the vertical line that passes through the vertex of the parabola.\newlineCalculation: The axis of symmetry is x=7x = 7.
  4. Increasing and Decreasing Intervals: d) Intervals where ff is increasing and decreasing are determined by the sign of the leading coefficient and the vertex.\newlineCalculation: Since the leading coefficient is negative, the parabola opens downwards. This means ff is increasing to the left of the vertex and decreasing to the right of the vertex.
  5. Domain Determination: e) Domain of any quadratic function is all real numbers.\newlineCalculation: Domain is (−∞,∞)(-\infty, \infty).
  6. Range Calculation: f) Range is determined by the vertex and the direction the parabola opens.\newlineCalculation: Since the parabola opens downwards and the vertex is at (7,2)(7, 2), the range is (−∞,2](-\infty, 2].

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