Answer:
y
=
x
2
−
10
x
+
2
is the equation of a parabola which will open upwards(because of the positive coefficient of
x
2
)
So it will have a Minimum
The Slope of this parabola is
d
y
d
x
=
2
x
−
10
and this slope is equal to zero at the vertex
2
x
−
10
=
0
→
2
x
=
10
→
x
=
5
The X coordinate of the vertex will be
5
y
=
5
2
−
10
(
5
)
+
2
=
25
−
50
+
2
=
−
23
The vertex is at
(
5
,
−
23
)
and has a Minimum Value
−
23
at this point.
The axis of symmetry is
x
=
5
The domain will be
∈
R
(all real numbers)
The range of this equation is
{
y
∈
R
:
y
≥
−
23
}
To get the x intercepts, we substitute y = 0
x
2
−
10
x
+
2
=
0
We get two x intercepts as
(
5
+
√
23
)
and
(
5
−
√
23
)
To get the Y intercepts, we substitute x = 0
y
=
0
2
−
10
⋅
0
+
2
=
2
We get the Y intercept as
2
This is how the Graph will look:
graph{x^2-10x+2 [-52.03, 52.03, -26, 26]}
explanation:
I HOPE IT HELPS
