the equation of a parabola in
vertex form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
y
=
a
(
x
−
h
)
2
+
k
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−−
where
(
h
,
k
)
are the coordinates of the vertex and a
is a multiplier
to obtain this form
complete the square
y
=
x
2
+
2
(
4
)
x
+
16
−
16
+
14
⇒
y
=
(
x
+
4
)
2
−
2
←
in vertex form
⇒
vertex
=
(
−
4
,
−
2
)
to obtain the intercepts
∙
let x = 0, in the equation for y-intercept
∙
let y = 0, in the equation for x-intercept
x
=
0
⇒
y
=
0
+
0
+
14
=
14
←
y-intercept
y
=
0
⇒
(
x
+
4
)
2
−
2
=
0
←
add 2 to both sides
⇒
(
x
+
4
)
2
=
2
take the square root of both sides
√
(
x
+
4
)
2
=
±
√
2
←
note plus or minus
⇒
x
+
4
=
±
√
2
←
subtract 4 from both sides
⇒
x
=
−
4
±
√
2
←
exact values
graph{(y-x^2-8x-14)((x+4)^2+(y+2)^2-0.04)=0 [-10, 10, -5, 5]}
Answer:
the expression is: 
and 2730 different ways are possible.
Step-by-step explanation:
In the given question we have to choose a president, vice
president, and secretary.
Permutations are used when order is important so, as in the given question order is required. We would use permutations
The formula used is:
where:
n=total number of objects
r=number of objects selected
In our case: n=15, r=3
Putting values and finding the answer:

So, the expression is: 
and 2730 different ways are possible.
Answer:
The euation of the linear function is:
Step-by-step explanation:
As the function has the values
Thus, the two points are:
Finding the slope between (5, -1) and (0, -1)




We know that the slope-intercept form of the line equation is
y=mx+b
where m is the slope and b is the y-intercept
We also know that the y-intercept can be computed by setting x=0 and finding the corresponding value of y.
so at x = 0, y = -1
Thus, the y-intercept 'b' = -1
Now, substituting m = 0 and b = -1 in the slope-intercept form of the line equation
y = mx+b
y = 0x + -1
y = -1
Therefore, the euation of the linear function is: