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If y=(1)/(3)(x-2)^(2) is graphed in the xy-plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation? I. x-intercept(s) II. y-intercept III. x-coordinate of the line of symmetry Choose 1 answer: (A) I only (B) I and II only (C) I and III only (D) I, II, and III

If y=13(x−2)2 y=\frac{1}{3}(x-2)^{2} is graphed in the xy x y -plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation?\newlineI. x x -intercept(s)\newlineII. y y -intercept\newlineIII. x x -coordinate of the line of symmetry\newlineChoose 11 answer:\newline(A) I only\newline(B) I and II only\newline(C) I and III only\newline(D) I, II, and III

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Q. If y=13(x−2)2 y=\frac{1}{3}(x-2)^{2} is graphed in the xy x y -plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation?\newlineI. x x -intercept(s)\newlineII. y y -intercept\newlineIII. x x -coordinate of the line of symmetry\newlineChoose 11 answer:\newline(A) I only\newline(B) I and II only\newline(C) I and III only\newline(D) I, II, and III
  1. Analyze Equation Characteristics: Analyze the given equation y=13(x−2)2y=\frac{1}{3}(x-2)^2 to determine the characteristics of its graph.
  2. Line of Symmetry: The xx-coordinate of the line of symmetry for a parabola in the form y=a(x−h)2+ky=a(x-h)^2+k is hh. In the given equation, h=2h=2, which means the line of symmetry is x=2x=2. This is directly given by the coefficient in the equation.
  3. Y-Intercept Calculation: The y-intercept occurs when x=0x=0. To find the y-intercept, substitute x=0x=0 into the equation and solve for yy.y=(13)(0−2)2y=\left(\frac{1}{3}\right)(0-2)^2y=(13)(−2)2y=\left(\frac{1}{3}\right)(-2)^2y=(13)(4)y=\left(\frac{1}{3}\right)(4)y=43y=\frac{4}{3}The y-intercept is not directly given as a constant or coefficient in the equation; it is a result of evaluating the function at x=0x=0.
  4. X-Intercept Calculation: The xx-intercepts occur when y=0y=0. Set the equation equal to zero and solve for xx. \newline0=(13)(x−2)20=\left(\frac{1}{3}\right)(x-2)^2\newlineSince (x−2)2(x-2)^2 is always non-negative, the only solution for this equation is when x−2=0x-2=0, which gives x=2x=2. This means there is only one xx-intercept, and it coincides with the line of symmetry. However, the xx-intercept is not displayed as a constant or coefficient in the equation; it is a result of solving the equation when y=0y=0.

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