Question

Consider the following quadratic equation. f(x) = 9x^2

Part A: Write a function, g(x), the shifts f(x) down by 3 units.
Part B: Write a function, h(x), that vertically stretches f(x) by 6 units.
Part C: Write a function, m(x), that reflects f(x) about the x-axis.

Answer 1

To modify the quadratic function
`f(x) = 9x^2`, for shifting down by 3 units use
`g(x) = 9x^2 - 3`, for stretching vertically by 6 units use
`h(x) = 54x^2`, and for reflecting about the x-axis use
`m(x) = -9x^2.`

Step-by-step explanation:

The student has asked about transforming a quadratic equation
`f(x) = 9x^2.`

Part A

To shift the function down by 3 units, we subtract 3 from the original function, giving us
`g(x) = 9x^2 - 3.`

Part B

For a vertical stretch by 6 units, we multiply the original function by 6, resulting in
`h(x) = 6 \(\cdot\) 9x^2 = > h(x) = 54x^2.`

Part C

To reflect the function about the x-axis, we multiply the function by -1, so
`m(x) = -9x^2.`