(-2, 0) (0, -2) (0, 2) find the formula for this cubic equation

We are given three points: \((-2, 0)\), \((0, -2)\), and \((0, 2)\), and we are tasked with finding a cubic equation that passes through these points.

Let the general form of the cubic equation be:

\[
y = ax^3 + bx^2 + cx + d
\]

### Step 1: Substitute the given points into the cubic equation.

#### Point 1: \((-2, 0)\)
\[
0 = a(-2)^3 + b(-2)^2 + c(-2) + d
\]
\[
0 = -8a + 4b - 2c + d \quad \text{(Equation 1)}
\]

#### Point 2: \((0, -2)\)
\[
-2 = a(0)^3 + b(0)^2 + c(0) + d
\]
\[
-2 = d \quad \text{(Equation 2)}
\]

#### Point 3: \((0, 2)\)
\[
2 = a(0)^3 + b(0)^2 + c(0) + d
\]
\[
2 = d \quad \text{(Equation 3)}
\]

### Step 2: Solve for the unknowns.

From Equations 2 and 3, we observe that there is a contradiction because \(d\) cannot be both \(-2\) and \(2\) simultaneously.

It seems the points provided might need some clarification since a cubic equation can’t pass through both \((0, -2)\) and \((0, 2)\) with a single value of \(d\).

Would you like to adjust the points or further investigate a different type of polynomial? Let me know if you'd like further clarification! 

### Further questions:
1. Could you check if any points need adjustment?
2. Would you like to explore different types of functions (e.g., quadratic)?
3. Do you want a graph of these points for visualization?
4. Should I attempt solving this using a system of equations for another scenario?
5. Would adding more points be helpful for better precision?

### Tip:
Always verify if the points provided make sense for the type of function you're dealing with, especially when dealing with higher-degree polynomials.

Explore how to find the cubic equation that passes through the points (-2, 0), (0, -2), and (0, 2). Learn the algebraic process of solving systems of equations to derive the cubic formula y = ax^3 + bx^2 + cx + d. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation