Sonia graphs the equation y=-x^2+4x and y=x-4 to solve the equation -x^2+4x=x-4. Her graph is shown below.
what are the solutions of -x^2+4x=x-4?
a)-5 and 0
b)-5 and -1
c)-1 and 4
d)0 and 4

−
x
2
+
4
x
=
x
−
4
-
x
2
+
4
x
=
x
-
4
Move all terms to the left side of the equation and simplify.
Tap for more steps...
−
x
2
+
3
x
+
4
=
0
-
x
2
+
3
x
+
4
=
0
Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
-
b
±
b
2
-
4
(
a
c
)
2
a
Substitute the values
a
=
−
1
a
=
-
1
,
b
=
3
b
=
3
, and
c
=
4
c
=
4
into the quadratic formula and solve for
x
x
.
−
3
±
√
3
2
−
4
⋅
(
−
1
⋅
4
)
2
⋅
−
1
-
3
±
3
2
-
4
⋅
(
-
1
⋅
4
)
2
⋅
-
1
Simplify.
Tap for more steps...
x
=
3
±
5
2
x
=
3
±
5
2
The final answer is the combination of both solutions.
x
=
4
,
−
1

Ithink the answer is a