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

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Find equations of tangent lines using limits

Full solution

Q. If

y=(x-1)(x+5)

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant in the equation?

\newline

Choose

1

answer:

\newline

A

x

-coordinate of the vertex

\newline

B

x

-intercept(s)

\newline

(C) Maximum

y

-value

\newline

(D)

y

-intercept

Understand Equation: First, let's understand the equation $y=(x-1)(x+5)$ . This is a quadratic equation in factored form. The graph of a quadratic equation is a parabola. The $x$ -intercepts of the graph can be found by setting $y$ to zero and solving for $x$ . Let's find the $x$ -intercepts. $\newline$ $y = (x - 1)(x + 5) = 0$ $\newline$ To find the $x$ -intercepts, we set each factor equal to zero and solve for $x$ . $\newline$ $x - 1 = 0$ or $x + 5 = 0$ $\newline$ $x$ $0$ or $x$ $1$
Find Intercepts: Now, let's find the y-intercept. The y-intercept occurs where the graph crosses the y-axis, which is when $x = 0$ . Let's substitute $x = 0$ into the equation to find the y-intercept. $y = (0 - 1)(0 + 5)$ $y = (-1)(5)$ $y = -5$ The y-intercept is the point $(0, -5)$ .
Vertex Calculation: The $x$ -coordinate of the vertex of a parabola in standard form $y = ax^2 + bx + c$ can be found using the formula $-\frac{b}{2a}$ . 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 $x$ -coordinate of the vertex is not the answer.
Maximum Y-Value: The maximum $y$ -value of a parabola occurs at the vertex. Since the coefficient of the $x^2$ term would be positive (if we were to expand the factored form), this parabola opens upwards, meaning it does not have a maximum $y$ -value; instead, it has a minimum $y$ -value. Therefore, the maximum $y$ -value is not the answer.
Final Answer: We have determined that the x-intercepts are the points where $x = 1$ and $x = -5$ , and the y-intercept is the point $(0, -5)$ . 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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