https://file.aiquickdraw.com/mathbot/file/1725837396469xzs1c6q1.jpg

To find a cubic function that fits the curve in the image, we will use the general form of a cubic function:

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

Given the points on the curve, we can substitute them into the equation to create a system of equations to solve for the coefficients \(a\), \(b\), \(c\), and \(d\).

From the image, we can identify two key points:
1. The curve passes through the origin: \((0, 0)\).
2. The curve passes through the point \((4, 14)\).

### Step 1: Set up equations using the known points

Substituting the point \((0, 0)\) into the cubic equation:

\[
0 = a(0)^3 + b(0)^2 + c(0) + d \implies d = 0.
\]

So, the cubic function simplifies to:

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

Substitute the point \((4, 14)\):

\[
14 = a(4)^3 + b(4)^2 + c(4).
\]

Simplifying:

\[
14 = 64a + 16b + 4c.
\]

### Step 2: Use additional information

To determine the coefficients accurately, we would typically need additional points or information about the curve (like a point where it changes direction, or information about its slope at certain points). 

If there are no additional points visible on the graph, we might not have enough information to uniquely determine the cubic function. However, the above equation provides a relation between \(a\), \(b\), and \(c\) based on the known point.

Would you like to provide additional information or use other methods to estimate the cubic function more accurately?

Find cubic function based on the curve passing through (0, 0) and (4, 14).

Learn how to find a cubic function that fits a curve passing through points (0, 0) and (4, 14). The problem involves using a general cubic equation y = ax^3 + bx^2 + cx + d, setting up a system of equations, and solving for coefficients. Suitable for students in Grades 10-12.

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