Step-by-step explanation:
Find the Center and Radius (x-4)^2+y^2=4
(
x
−
4
)
2
+
y
2
=
4
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r
=
2
h
=
4
k
=
0
The center of the circle is found at
(
h
,
k
)
.
Center:
(
4
Answer:
y = 
Step-by-step explanation:
Given
5x - 8y = 11 ( subtract 5x from both sides )
- 8y = 11 - 5x ( multiply through by - 1 )
8y = - 11 + 5x = 5x - 11 ( divide both sides by 8 )
y = 
(2x/-5x)+x^2
(x(2)/(x(-5))+x^2
(-2/5)+x^2, the x values cancel in numerator and denominator and simplify to -2/5
We have been given a parent function
and we need to transform this function into
.
We will be required to use three transformations to obtain the required function from
.
First transformation would be to shift the graph to the right by 4 units. Upon using this transformation, the function will change to
.
Second transformation would be to compress the graph vertically by half. Upon using the second transformation, the new function becomes
.
Third transformation would be to shift the graph upwards by 5 units. Upon using this last transformation, we get the new function as
.