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Use the graph and the factor theorem to list the factors of
f(x).
For the toolbar, press
ALT+F 10(PC) or
ALT+FN+F 10(Mac)

Use the graph and the factor theorem to list the factors of $f(x)$ . $\newline$ For the toolbar, press $A L T+F 10(P C)$ or $A L T+F N+F 10(\mathrm{Mac})$

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Write equations of parabolas in vertex form using properties

Full solution

Q. Use the graph and the factor theorem to list the factors of

f(x)

.

\newline

For the toolbar, press

A L T+F 10(P C)

or

A L T+F N+F 10(\mathrm{Mac})

Find $X$ -Intercepts: Look at the graph to find the $x$ -intercepts, which are the points where the graph crosses the $x$ -axis. These $x$ -values are the roots of the polynomial $f(x)$ .
Apply Factor Theorem: If the graph crosses the x-axis at $x = a$ , then $(x - a)$ is a factor of $f(x)$ according to the factor theorem.
Identify Intercepts: Identify all the $x$ -intercepts from the graph. Let's say they are $x = p$ , $x = q$ , and $x = r$ .
Write Down Factors: Write down the factors corresponding to each $x$ -intercept. So the factors are $(x - p)$ , $(x - q)$ , and $(x - r)$ .
Verify Factors: Check if each factor corresponds to an actual $x$ -intercept on the graph to ensure no mistakes were made.

More problems from Write equations of parabolas in vertex form using properties

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Question

In which direction does the parabola

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\newline

\text{up}

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What is the vertex of the parabola

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?

\newline

(\_,\_)

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What is the axis of symmetry of the parabola

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Question

In which direction does the parabola

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\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

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\text{[D]left}

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\newline

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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

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(D) The center is

(0,-4)

and the radius is

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Posted 4 months ago

Question

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

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

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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