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y=(x-3)(x+9)
The given equation is graphed in the
xy-plane. Which of the following are
x-intercepts of the graph?
Choose 1 answer
(A) -3 and -9
(B) -3 and 9
(C) 3 and -9
(D) 3 and 9

$y=(x-3)(x+9)$ $\newline$ The given equation is graphed in the $x y$ -plane. Which of the following are $x$ -intercepts of the graph? $\newline$ Choose $1$ answer: $\newline$ (A) $-3$ and $-9$ $\newline$ (B) $-3$ and $9$ $\newline$ (C) $3$ and $-9$ $\newline$ (D) $3$ and $9$

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Identify the direction a parabola opens

Full solution

Q.

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

Choose

1

answer:

\newline

(A)

-3

and

-9

\newline

(B)

-3

and

9

\newline

(C)

3

and

-9

\newline

(D)

3

and

9

Understanding x-intercepts: Understand the concept of x-intercepts. $\newline$ The x-intercepts of a graph are the points where the graph crosses the x-axis. At these points, the value of $y$ is $0$ .
Setting the equation equal to zero: Set the equation $y=(x-3)(x+9)$ equal to $0$ to find the x-intercepts. $\newline$ $0 = (x-3)(x+9)$
Solving for x: Solve for x to find the x-intercepts. $\newline$ We have a product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero: $\newline$ $x - 3 = 0$ or $x + 9 = 0$
Concluding the x-intercepts: Solve each equation for x. $\newline$ $x - 3 = 0$ gives $x = 3$ $\newline$ $x + 9 = 0$ gives $x = -9$
Concluding the x-intercepts: Solve each equation for x. $\newline$ $x - 3 = 0$ gives $x = 3$ $\newline$ $x + 9 = 0$ gives $x = -9$ Conclude the x-intercepts. $\newline$ The x-intercepts of the graph are $x = 3$ and $x = -9$ .

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