Question

What is the new vertex of the function after the transformation?



(4 points)
Write your answer as an ordered pair.

#1 Find the vertex of the function f(x)=x2
after the positive horizontal shift 4 units
#2 Find the vertex of the function f(x)=x2
after the positive vertical shift 5 units
#3 Find the vertex of the function f(x)=x2
after the negative horizontal shift 3 units
#4 Find the vertex of the function f(x)=x2
after the negative vertical shift 2 units

Answer 1

To determine the new vertex of the function \( f(x) = x^2 \) after the specified transformations, we start with the vertex of the original function, which is at the point \( (0, 0) \).

### #1 Positive horizontal shift 4 units:
A horizontal shift of 4 units to the right changes the function to:
\[
f(x) = (x - 4)^2
\]
The vertex after this shift will be:
\[
(4, 0)
\]

### #2 Positive vertical shift 5 units:
A vertical shift of 5 units upward changes the function to:
\[
f(x) = x^2 + 5
\]
The vertex after this shift will be:
\[
(0, 5)
\]

### #3 Negative horizontal shift 3 units:
A horizontal shift of 3 units to the left changes the function to:
\[
f(x) = (x + 3)^2
\]
The vertex after this shift will be:
\[
(-3, 0)
\]

### #4 Negative vertical shift 2 units:
A vertical shift of 2 units downward changes the function to:
\[
f(x) = x^2 - 2
\]
The vertex after this shift will be:
\[
(0, -2)
\]

### Summary of New Vertices:
1. After positive horizontal shift 4 units: **(4, 0)**
2. After positive vertical shift 5 units: **(0, 5)**
3. After negative horizontal shift 3 units: **(-3, 0)**
4. After negative vertical shift 2 units: **(0, -2)**