Question

Write a quadratic equation with the given transformations from the Parent function: y=x²

a. Horizontal shift 8 units to the right.
b. Reflection across the x-axis.
c. Vertical compression by a factor of (1)/(3).
d. Vertical shift down 5 units

Answer 1

To create a quadratic equation with the specified transformations from the parent function y=x², apply a horizontal shift, a reflection, a vertical compression, and a vertical shift to get y = -(1/3)(x-8)² - 5.

Step-by-step explanation:

To write a quadratic equation with the given transformations from the parent function y=x², we need to apply each transformation one by one:

a. Horizontal shift 8 units to the right is represented by (x-8).

b. Reflection across the x-axis is represented by multiplying the function by -1.

c. Vertical compression by a factor of 1/3 is represented by multiplying the function by 1/3.

d. Vertical shift down 5 units is represented by subtracting 5 from the function.

All these transformations applied to the parent function y=x² give us the following quadratic equation:

y = -(1/3)(x-8)² - 5