Question

The question is in the image

Answer 1

First, identify the parent function. Note that the given function is a quadratic in Vertex Form, so the parent function would simply be a quadratic:

g(x)=x^2 is the parent function. This is the most basic parabola, and transformations are added to alter the function’s lateral and vertical location and width or length.

Now that we have the parent function, let’s address the transformations done to it. Remember, when identifying transformations, remover to follow PEMDAS; act like you are inputting a value in for x and following PEMDAS to observe how the function is altered.

• Lateral shift 3 units to the right

*Remember, horizontal translations have opposite signs, so even though x is subtracted by 3, it will actually move to the right towards the positive direction.

•Reflect over the x-axis

•Shrink by a factor of 1/2

*This will produce a wide parabola

• Vertical shift up 12 units

Answer 2

1. The negative flips the parabola upside down so there is a maximum

2. The 1/2 means there is a vertical shrink

3. -3 means the graph moves to the RIGHT 3 units (X sign always changes)

4. +12 means the graph shifts up 12 units

Explanation: