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

Understanding Standard Form: To find the characteristic of the graph that is displayed as a constant in the equation, we need to understand the standard form of a quadratic equation, which is y = ax^2 + bx + c. The constant term in this form is 'c', which represents the y-intercept of the graph.Identifying the Constant Term: Let's identify the constant term in the given equation y = (x-1)(x+5). To do this, we need to expand the equation. y = x^2 + 5x - x - 5 y = x^2 + 4x - 5 The constant term here is '-5'.Interpreting the Constant Term: The constant term '-5' in the expanded form of the equation y = x^2 + 4x - 5 represents the y-intercept of the graph. This is the point where the graph crosses the y-axis.Characteristics of the Graph: The x-coordinate of the vertex, x-intercepts, and maximum y-value are not constants in the equation; they depend on the values of 'a', 'b', and 'c' and the shape of the parabola. However, the y-intercept is directly given by the constant term 'c' in the equation y = ax^2 + bx + c.

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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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Math Problems

Algebra 1

Domain and range of quadratic functions: equations

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

y

-value

\newline

(D)

y

-intercept

Understanding Standard Form: To find the characteristic of the graph that is displayed as a constant in the equation, we need to understand the standard form of a quadratic equation, which is $y = ax^2 + bx + c$ . The constant term in this form is ' $c$ ', which represents the $y$ -intercept of the graph.
Identifying the Constant Term: Let's identify the constant term in the given equation $y = (x-1)(x+5)$ . To do this, we need to expand the equation. $y = x^2 + 5x - x - 5$ $y = x^2 + 4x - 5$ The constant term here is ' $-5$ '.
Interpreting the Constant Term: The constant term ' $-5$ ' in the expanded form of the equation $y = x^2 + 4x - 5$ represents the y-intercept of the graph. This is the point where the graph crosses the y-axis.
Characteristics of the Graph: The $x$ -coordinate of the vertex, $x$ -intercepts, and maximum $y$ -value are not constants in the equation; they depend on the values of ' $a$ ', ' $b$ ', and ' $c$ ' and the shape of the parabola. However, the $y$ -intercept is directly given by the constant term ' $c$ ' in the equation $y = ax^2 + bx + c$ .