Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $9$

View step-by-step help

View step-by-step help

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 $x = -9$ .

More problems from Identify the direction a parabola opens

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

Posted 2 months ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 3 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 3 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 3 months ago

Question

What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

Posted 3 months ago

Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Posted 3 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 2 months ago

Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

(0,4)

and the radius is

1

\newline

(D) The center is

(0,-4)

and the radius is

1

Posted 4 months ago

Question

y=2 x^{2}-5 x+7

is graphed in the

x y

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

\newline

1

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

-coordinate of the vertex

Posted 4 months ago

Question

Harper uploaded a funny video of her dog onto a website. The relationship between the elapsed time,

d

, in days, since the video was first uploaded, and the total number of views,

V(d)

, that the video received is modeled by the following function.

V(d) = 4^{1.25d}

. How many views will the video receive after

6

days? Round your answer, if necessary, to the nearest hundredth.

Posted 31 minutes ago