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

Question

(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 find the vertex of the function \( f(x) = x^2 \) after various transformations, let's start with the original vertex of the function, which is at the point \( (0, 0) \).

The transformations we will apply are horizontal and vertical shifts.

#1 Positive Horizontal Shift 4 Units

A positive horizontal shift of 4 units moves the vertex 4 units to the right. The new vertex will be: \[ (0 + 4, 0) = (4, 0) \]

#2 Positive Vertical Shift 5 Units

A positive vertical shift of 5 units moves the vertex 5 units up. The new vertex after this shift will be: \[ (0, 0 + 5) = (0, 5) \]

#3 Negative Horizontal Shift 3 Units

A negative horizontal shift of 3 units moves the vertex 3 units to the left. The new vertex will be: \[ (0 - 3, 0) = (-3, 0) \]

#4 Negative Vertical Shift 2 Units

A negative vertical shift of 2 units moves the vertex 2 units down. The new vertex after this shift will be: \[ (0, 0 - 2) = (0, -2) \]

Summary of New Vertices

1. After a positive horizontal shift of 4 units: \( (4, 0) \)
2. After a positive vertical shift of 5 units: \( (0, 5) \)
3. After a negative horizontal shift of 3 units: \( (-3, 0) \)
4. After a negative vertical shift of 2 units: \( (0, -2) \)