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If y=2x^(2)-5x+7 is graphed in the xy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation? Choose 1 answer: (A) x-intercept(s) (B) y-intercept (C) x-coordinate of the vertex (D) y-coordinate of the vertex

If y=2x2−5x+7 y=2 x^{2}-5 x+7 is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) x x -intercept(s)\newline(B) y y -intercept\newline(C) x x -coordinate of the vertex\newline(D) y y -coordinate of the vertex

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Q. If y=2x2−5x+7 y=2 x^{2}-5 x+7 is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) x x -intercept(s)\newline(B) y y -intercept\newline(C) x x -coordinate of the vertex\newline(D) y y -coordinate of the vertex
  1. Identify characteristics of parabola: Identify the characteristics of a parabola that can be directly read from the standard form equation y=ax2+bx+cy = ax^2 + bx + c.
  2. Recognize y-intercept of parabola: Recognize that the y-intercept of a parabola is the point where the graph crosses the y-axis, which occurs when x=0x = 0.
  3. Substitute x=0x = 0 to find y-intercept: Substitute x=0x = 0 into the equation y=2x2−5x+7y = 2x^2 - 5x + 7 to find the y-intercept.\newliney=2(0)2−5(0)+7y = 2(0)^2 - 5(0) + 7\newliney=0−0+7y = 0 - 0 + 7\newliney=7y = 7
  4. Conclude y-intercept from constant term: Conclude that the y-intercept is the constant term in the equation of the parabola, which is 77 in this case.
  5. Match y-intercept to given options: Match the characteristic to the options given in the problem.\newlineThe y-intercept is displayed as a constant in the equation, which corresponds to option BB.

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