Question

Explain the steps (in order) of how to create this function f (x) = 3( x-5)^2/ 7

Answer 1

To create f(x) = 3(x-5)^2/7, start with the base function x^2, shift it right by 5 units, stretch vertically by a factor of 3, and then compress vertically by dividing by 7.

Step-by-step explanation:

To create the function f(x) = \frac{3(x-5)^2}{7}, follow these steps:

1. Identify the base function, which is x^2. This function represents a parabola that opens upwards.
2. Modify the base function by incorporating a horizontal shift. The term (x-5) indicates a shift of the parabola 5 units to the right.
3. Next, adjust the vertical stretch of the parabola by multiplying the entire function by the coefficient 3. This makes the parabola narrower or wider depending on whether the coefficient is greater than or less than 1.
4. Finally, apply a vertical compression by dividing the function by 7. This scales down the parabola, making it less steep.

The function f(x) now represents a parabola that is shifted 5 units to the right, vertically stretched by a factor of 3, and compressed vertically by a factor of 7.