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]}
Point C(0,3) is the y intercept because it's where x=0
Answer:
x, y = 7, 1
Step-by-step explanation:
x+6y=13 ............ (i)
2x+y=15 ........... (ii)
We will apply substitute method.
From equation (i), we can get,
x+6y=13
or, x = 13 - 6y .......... (iii)
Putting the value of x in equation (ii), we can get,
2x+y=15
or, 2 × (13 - 6y) + y = 15
or, 26 - 12 y + y = 15 [multiplying]
or, -11 y = 15 - 26 [Subtracting 26 from both the sides]
or, -11 y = -11
or, [(-11 y) ÷ (-11)] = [(-11) ÷ (-11)] [Dividing both the sides by -11]
or, y = 1
Therefore, the value of y = 1
Putting y = 1 in equation (iii), we get,
x = 13 - 6y
or, x = 13 - 6 × 1
or, x = 13 - 6
or, x = 7
Therefore, the value of x = 7.
Answer: x, y = 7, 1
The number line M-N is from 0 - 9.
2/3 of the way will be the same as 9 x 2/3
That equals 18/3 which reduces to 6.
6 is the coord 2/3 across the numberline from 0 to 9.
