Question

part iii. transforming quadratic functions

1. transform using the parent function (f(x) = x^2), create four new functions based on the parent function, one for each of the transformations below.

a. vertical shift, such as (f(x) + k), for some constant, k

b. horizontal shift, such as (f(x - h)), for some constant, h

c. vertical stretch/compression, such as (a \cdot f(x)), for some constant, a

d. reflection, such as (-f(x))

Explanation:

Define the parent function and transformation rules

$$
LATEXBLOCK0
$$

Create specific transformed functions

$$
LATEXBLOCK1
$$

Answer:

a. Vertical Shift (using \(k = 3\)):

$$g(x) = x^2 + 3$$

b. Horizontal Shift (using \(h = 2\)):

$$g(x) = (x - 2)^2$$

c. Vertical stretch/compression (using \(a = 2\)):

$$g(x) = 2x^2$$

d. Reflection:

$$g(x) = -x^2$$