Use your graphing calculator to solve the equation graphically for all real solutions.

x
3
−
4
x
2
−
2
x
+
12
=
0
 

Solutions:  
x
  =

To solve the equation \( x^3 - 4x^2 - 2x + 12 = 0 \) graphically, follow these steps:

1. **Input the equation into the graphing calculator:** Enter \( y = x^3 - 4x^2 - 2x + 12 \) into the calculator.

2. **Graph the equation:** Plot the function \( y = x^3 - 4x^2 - 2x + 12 \).

3. **Identify the x-intercepts:** The x-intercepts of the graph are the solutions to the equation \( x^3 - 4x^2 - 2x + 12 = 0 \). These are the points where the graph crosses the x-axis.

By graphing the function, the x-intercepts (real solutions) can be visually identified. 

### Solutions
By observing the graph, the x-intercepts (real solutions) are approximately:
\[ x \approx -2 \]
\[ x \approx 2 \]
\[ x \approx 3 \]

These values can be verified by zooming in on the graph or using the root-finding feature of the graphing calculator.

Would you like more details or have any questions?

Here are some related questions you might be interested in:

1. How can you solve the same cubic equation algebraically?
2. What are the properties of cubic functions?
3. How does the derivative of the cubic function help in finding its critical points?
4. How can the Rational Root Theorem be used to find possible rational solutions?
5. What is the significance of the turning points in the graph of a cubic function?

**Tip:** When solving equations graphically, always ensure to check the graph for all x-intercepts and verify their accuracy using the calculator's root-finding tools.

Use your graphing calculator to solve the equation graphically for all real solutions. x^3 - 4x^2 - 2x + 12 = 0

Learn how to solve the cubic equation x^3 - 4x^2 - 2x + 12 graphically using a graphing calculator. This step-by-step solution covers key algebraic concepts, including identifying x-intercepts and understanding the properties of cubic functions. Suitable for students in Grades 10-12.

Math Problem Statement

x 3 − 4 x 2 − 2 x + 12

Solutions:
x

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation