Math / Algebra

QuestionFind approximate (to 3 decimal places) solutions to $3 x^{3}-2 x^{2}-6 x+4=0$ by graphing the polynomial. Write your answers in ascending order. $x=$ $\begin{array}{l} x= \\ x= \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to find where the graph of this curvy cubic equation $3x^3 - 2x^2 - 6x + 4$ crosses the x-axis, and we only need to be about 3 decimals accurate! Watch out! Make sure your graph is zoomed in enough around the x-axis crossings to get those decimal places right!

STEP 2

1. Define the function
2. Graph the function
3. Find the x-intercepts

STEP 3

Let's define our function as $f(x) = 3x^3 - 2x^2 - 6x + 4$ .
This tells us the y-value of our graph for any x-value we plug in!

STEP 4

Now, we need to graph this function.
We're looking for where this graph crosses the x-axis.
Those are the solutions we're after!
You can use a graphing calculator or an online graphing tool.
Just make sure you can zoom in!

STEP 5

Look closely at where the graph crosses the x-axis.
These are the points where $f(x) = 0$ , which are the solutions to our equation!
We need to find the x-values of these points.

STEP 6

Let's zoom in on the graph near the first crossing, the one furthest to the left.
It looks like it crosses around $x =$ -1.215.

STEP 7

Now, let's zoom in on the middle crossing.
It looks like it crosses around $x =$ 0.667.

STEP 8

Finally, let's zoom in on the last crossing, the one furthest to the right.
It looks like it crosses around $x =$ 1.548.

STEP 9

So, our approximate solutions, in ascending order, are $x \approx$ -1.215, $x \approx$ 0.667, and $x \approx$ 1.548.
Boom!

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QuestionFind approximate (to 3 decimal places) solutions to $3 x^{3}-2 x^{2}-6 x+4=0$ by graphing the polynomial. Write your answers in ascending order. $x=$ $\begin{array}{l} x= \\ x= \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to find where the graph of this curvy cubic equation $3x^3 - 2x^2 - 6x + 4$ crosses the x-axis, and we only need to be about 3 decimals accurate! Watch out! Make sure your graph is zoomed in enough around the x-axis crossings to get those decimal places right!

STEP 2

1. Define the function
2. Graph the function
3. Find the x-intercepts

STEP 3

Let's define our function as $f(x) = 3x^3 - 2x^2 - 6x + 4$ .
This tells us the y-value of our graph for any x-value we plug in!

STEP 4

Now, we need to graph this function.
We're looking for where this graph crosses the x-axis.
Those are the solutions we're after!
You can use a graphing calculator or an online graphing tool.
Just make sure you can zoom in!

STEP 5

Look closely at where the graph crosses the x-axis.
These are the points where $f(x) = 0$ , which are the solutions to our equation!
We need to find the x-values of these points.

STEP 6

Let's zoom in on the graph near the first crossing, the one furthest to the left.
It looks like it crosses around $x =$ -1.215.

STEP 7

Now, let's zoom in on the middle crossing.
It looks like it crosses around $x =$ 0.667.

STEP 8

Finally, let's zoom in on the last crossing, the one furthest to the right.
It looks like it crosses around $x =$ 1.548.

STEP 9

So, our approximate solutions, in ascending order, are $x \approx$ -1.215, $x \approx$ 0.667, and $x \approx$ 1.548.
Boom!

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QuestionFind approximate (to 3 decimal places) solutions to 3x3−2x2−6x+4=03 x^{3}-2 x^{2}-6 x+4=03x3−2x2−6x+4=0 by graphing the polynomial. Write your answers in ascending order. x=x=x= x=x=\begin{array}{l} x= \\ x= \end{array}x=x=​

Studdy Solution

STEP 1

STEP 2

1. Define the function2. Graph the function3. Find the x-intercepts

STEP 3

Let's **define** our function as f(x)=3x3−2x2−6x+4f(x) = 3x^3 - 2x^2 - 6x + 4f(x)=3x3−2x2−6x+4.This tells us the *y*-value of our graph for any *x*-value we plug in!

STEP 4

Now, we need to **graph** this function.We're looking for where this graph crosses the *x*-axis.Those are the solutions we're after!You can use a graphing calculator or an online graphing tool.Just make sure you can zoom in!

STEP 5

Look closely at where the graph crosses the *x*-axis.These are the points where f(x)=0f(x) = 0f(x)=0, which are the solutions to our equation!We need to find the *x*-values of these points.

STEP 6

Let's zoom in on the graph near the first crossing, the one furthest to the left.It looks like it crosses around x=x = x=-**1.215**.

STEP 7

Now, let's zoom in on the middle crossing.It looks like it crosses around x=x =x=**0.667**.

STEP 8

Finally, let's zoom in on the last crossing, the one furthest to the right.It looks like it crosses around x=x =x=**1.548**.

STEP 9

So, our approximate solutions, in ascending order, are x≈x \approx x≈-**1.215**, x≈x \approx x≈**0.667**, and x≈x \approx x≈**1.548**.Boom!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind approximate (to 3 decimal places) solutions to $3 x^{3}-2 x^{2}-6 x+4=0$ by graphing the polynomial. Write your answers in ascending order. $x=$ $\begin{array}{l} x= \\ x= \end{array}$

1. Define the function
2. Graph the function
3. Find the x-intercepts

Let's define our function as $f(x) = 3x^3 - 2x^2 - 6x + 4$ .
This tells us the y-value of our graph for any x-value we plug in!

Now, we need to graph this function.
We're looking for where this graph crosses the x-axis.
Those are the solutions we're after!
You can use a graphing calculator or an online graphing tool.
Just make sure you can zoom in!

Look closely at where the graph crosses the x-axis.
These are the points where $f(x) = 0$ , which are the solutions to our equation!
We need to find the x-values of these points.

Let's zoom in on the graph near the first crossing, the one furthest to the left.
It looks like it crosses around $x =$ -1.215.

Now, let's zoom in on the middle crossing.
It looks like it crosses around $x =$ 0.667.

Finally, let's zoom in on the last crossing, the one furthest to the right.
It looks like it crosses around $x =$ 1.548.

So, our approximate solutions, in ascending order, are $x \approx$ -1.215, $x \approx$ 0.667, and $x \approx$ 1.548.
Boom!