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: $(0,-2)$