Given the function, check all the transformations that occurred from the graph of the parent function.

Question

* f(x)=1/2(x+7)^2+4
0/1
Captionless Image
up 7 units
up 4 units

down 7 units
down 4 units
left 7 units

left 4 units
right 7 units
right 4 units
vertical stretch
vertical compression
reflection x-axis
reflection y-axis

Answer 1

To analyze the transformations of the function \( f(x) = \frac{1}{2}(x + 7)^2 + 4 \) from the parent function \( g(x) = x^2 \) (which is a basic quadratic function), we can break down each transformation step by step.

1. Horizontal Shift: The expression \( (x + 7) \) indicates a left shift of 7 units. This happens because when you add a number inside the function (in this case, \( +7 \)), it shifts the graph left.

2. Vertical Compression: The factor \( \frac{1}{2} \) in front of the squared term indicates a vertical compression because it reduces the height of the graph by half. This means that the graph is "squished" vertically.

3. Vertical Shift: The \( +4 \) at the end indicates an upward shift of 4 units. This is simply moving the entire graph up by 4 units.

Thus, putting all of these transformations together, we have:

• Left 7 units
• Vertical compression (by a factor of \( \frac{1}{2} \))
• Up 4 units

So in summary, the transformations from the graph of the parent function \( x^2 \) to the graph of \( f(x) = \frac{1}{2}(x + 7)^2 + 4 \) are:

• Left 7 units
• Vertical compression
• Up 4 units

The correct answers based on the options provided are:

• Left 7 units
• Up 4 units
• Vertical compression