Answer:
(4, 1)
Step-by-step explanation:
x^2 + y^2 - 2y - 8x - 19 = 0
We rearrange the terms and complete the square twice.
x^2 - 8x + y^2 - 2y = 19
x^2 - 8x + 16 + y^2 - 2y + 1 = 19 + 16 + 1
(x - 4)^2 + (y - 1)^2 = 6^2
The center is (4, 1)
Answer:
f(x) = x² + 4x + 3
Step-by-step explanation:
Here in this problem, we have to find the quadratic function that has x = - 1 and x = - 3 as the only two real zeros.
So, from the above condition, we can say that (x + 1) and (x + 3) are the only two factors of the function.
Therefore, the function will be f(x) = (x + 1)(x + 3), such that if the function is zero, then the solutions will be x = - 1 and x = - 3.
Hence, f(x) = x² + 4x + 3 (Answer)
Answer:
- 
= 
Step-by-step explanation:
First, we have to convert the mixed fractions to improper fractions
= 
= 
= 
= 
- = 
- 
=
We cannot simplify so it is the final answer
Answer:
Vertex:
(
3
2
,
−
41
4
)
(
3
2
,
-
41
4
)
Focus:
(
3
2
,
−
10
)
(
3
2
,
-
10
)
Axis of Symmetry:
x
=
3
2
x
=
3
2
Directrix:
y
=
−
21
2
y
=
-
21
2
x
y
0
−
8
1
−
10
3
2
−
41
4
3
−
8
4
−
4
Vertex:
(
3
2
,
−
41
4
)
(
3
2
,
-
41
4
)
Focus:
(
3
2
,
−
10
)
(
3
2
,
-
10
)
Axis of Symmetry:
x
=
3
2
x
=
3
2
Directrix:
y
=
−
21
2
y
=
-
21
2
x
y
0
−
8
1
−
10
3
2
−
41
4
3
−
8
4
−
4
Step-by-step explanation:
