If $y=(x+2)(x+8)$ 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) $x$ -intercept(s) $\newline$ (B) $y$ -intercept $\newline$ (C) $x$ -coordinate of the vertex $\newline$ (D) Minimum $y$ -value

Full solution

Q. If

y=(x+2)(x+8)

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

-intercept(s)

\newline

(B)

y

-intercept

\newline

(C)

x

-coordinate of the vertex

\newline

(D) Minimum

y

-value

Understand Equation Form: To determine the characteristic of the graph that is constant in the equation, we need to understand the form of the equation $y=(x+2)(x+8)$ .
Identify X-Intercepts: The given equation is in factored form, which can help us identify the x-intercepts of the graph. The x-intercepts occur where $y=0$ , which would be at the values of $x$ that make each factor equal to zero. In this case, those values are $x=-2$ and $x=-8$ .
X-Intercepts Not Constants: However, the question asks for a constant in the equation. The $x$ -intercepts are not constants; they are the values of $x$ for which $y$ equals $0$ . Therefore, option $(A)$ is not the correct answer.
Find Y-Intercept: The y-intercept occurs where the graph crosses the y-axis, which is when $x=0$ . To find the y-intercept, we substitute $x=0$ into the equation and solve for $y$ .
Substitute $X=0$ : Substituting $x=0$ into the equation gives us $y=(0+2)(0+8)$ , which simplifies to $y=2\times 8$ .
Calculate $Y=16$ : Calculating the product gives us $y=16$ . This is the $y$ -intercept of the graph, and it is a constant in the equation because it does not change regardless of the value of $x$ .
Y-Intercept is Constant: Since the y-intercept is a constant and is represented in the equation when $x=0$ , the correct answer is option (B) y-intercept.