Answer:To move the equation y = x^3 + 4x^2 to the right, we can introduce a shift in the x-values. This is achieved by replacing x with (x - h), where h represents the amount of shift we want.
To move the equation to the right, we need to determine the value of h. The value of h will determine the new x-coordinate for each point on the graph. We want the graph to shift to the right, so we need to subtract h from x.
Here's how you can do it step-by-step:
1. Replace x with (x - h) in the equation:
y = (x - h)^3 + 4(x - h)^2
2. Expand the equation:
y = (x - h)(x - h)(x - h) + 4(x - h)(x - h)
3. Simplify the equation by multiplying:
y = (x - h)(x^2 - 2hx + h^2) + 4(x^2 - 2hx + h^2)
4. Distribute and combine like terms:
y = x^3 - 2hx^2 + h^2x - hx^2 + 2h^2x - h^3 + 4x^2 - 8hx + 4h^2
5. Collect like terms:
y = x^3 + (h^2 - 2h)x^2 + (2h^2 - 8h)x + (4h^2 - h^3)
By replacing x with (x - h), we have shifted the equation y = x^3 + 4x^2 to the right by h units. The coefficients in the equation have also changed due to the shift.
Please note that the equation may simplify further depending on the specific value of h. Remember to substitute the desired value of h into the equation to reflect the desired right shift.
Step-by-step explanation:
