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

If y=(x−1)(x+5) y=(x-1)(x+5) is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant in the equation?\newlineChoose 11 answer:\newline(A) x x -coordinate of the vertex\newline(B) x x -intercept(s)\newline(C) Maximum y y -value\newline(D) y y -intercept

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Q. If y=(x−1)(x+5) y=(x-1)(x+5) is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant in the equation?\newlineChoose 11 answer:\newline(A) x x -coordinate of the vertex\newline(B) x x -intercept(s)\newline(C) Maximum y y -value\newline(D) y y -intercept
  1. Understand Equation: First, let's understand the equation y=(x−1)(x+5)y=(x-1)(x+5). This is a quadratic equation in factored form. The graph of a quadratic equation is a parabola. The xx-intercepts of the graph can be found by setting yy to zero and solving for xx. Let's find the xx-intercepts.\newliney=(x−1)(x+5)=0y = (x - 1)(x + 5) = 0\newlineTo find the xx-intercepts, we set each factor equal to zero and solve for xx.\newlinex−1=0x - 1 = 0 or x+5=0x + 5 = 0\newlinexx00 or xx11
  2. Find Intercepts: Now, let's find the y-intercept. The y-intercept occurs where the graph crosses the y-axis, which is when x=0x = 0. Let's substitute x=0x = 0 into the equation to find the y-intercept.y=(0−1)(0+5)y = (0 - 1)(0 + 5)y=(−1)(5)y = (-1)(5)y=−5y = -5The y-intercept is the point (0,−5)(0, -5).
  3. Vertex Calculation: The xx-coordinate of the vertex of a parabola in standard form y=ax2+bx+cy = ax^2 + bx + c can be found using the formula −b2a-\frac{b}{2a}. However, our equation is not in standard form, and the vertex is not represented as a constant in the factored form of the equation. Therefore, the xx-coordinate of the vertex is not the answer.
  4. Maximum Y-Value: The maximum yy-value of a parabola occurs at the vertex. Since the coefficient of the x2x^2 term would be positive (if we were to expand the factored form), this parabola opens upwards, meaning it does not have a maximum yy-value; instead, it has a minimum yy-value. Therefore, the maximum yy-value is not the answer.
  5. Final Answer: We have determined that the x-intercepts are the points where x=1x = 1 and x=−5x = -5, and the y-intercept is the point (0,−5)(0, -5). The x-intercepts and the y-intercept are the characteristics of the graph that can be directly read from the equation. However, the question asks for the characteristic that is displayed as a constant in the equation. The y-intercept is the constant term that would appear when the equation is expanded, and it is the only characteristic among the options that is a constant in the equation.

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